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The Balance of Payments Constrained Growth Model with Sustainable Debt Accumulation, Interest Payments and the Terms of Trade:

Evidence from Sub-Saharan Africa.

Shanaz Sumra University of Greenwich

Abstract The relevance of a demand-led growth model for long run economic growth is tested for the sub-Saharan African region using an augmented balance of payments constrained growth model which allows for sustainable debt accumulation, interest rate payments and the terms of trade movements. An autoregressive distributive lag (ARDL) model is used to estimate the model for 22 sub-Saharan African economies. Different specifications of the balance of payments constrained growth model are estimated and compared. The results indicate that the region was balance of payments constrained between the 1960 to 2014 period. In addition, the model which allows for sustainable debt accumulation and interest rate payments abroad best explained the growth experience of the region.

Year: 2016

No: GPERC36

GREENWICH POLITICAL ECONOMY RESEARCH CENTRE (GPERC)

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Keywords: Balance of payments, constrained growth, debt, interest payments

abroad, terms of trade, sub-Saharan Africa

Acknowledgments: I would like to thank Ozlem Onaran (University of

Greenwich), for her valuable comments and suggestions. An earlier version of

the paper was presented at the 19th annual conference for The Research Network

Macroeconomics and Macroeconomic Policies, (Berlin/2015). Any remaining

errors remain mine.

JEL codes: 055, R11, F14, 011.

Corresponding author: Shanaz Sumra, University of Greenwich, Old Royal

Naval College, 30 Park Row, London

Email: [email protected]

mailto:[email protected]

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1. Introduction

The balance of payments constrained growth model has been tested extensively for developed

countries with the results generally giving support to it1. It has also been tested for several

developing countries particularly in Latin America and Asia (Alvarez-Ude and Gomez, 2008;

Bertola et al, 2002; Britto and McCombie, 2009; Moreno-Brid, 2003; Razmi, 2005; Felipe et

al, 2010; Tharnpanich and McCombie, 2013). There is very little empirical research regarding

the relevance of balance of payments constraints for sub-Saharan Africa. The few studies that

do exist on sub-Saharan Africa verify the theoretical expectations of the model (Hussain, 1999;

Nell, 2003; Perraton, 2003).

The last comprehensive study on the balance of payments constrained model for the African

region was done by Hussain (1999) using data covering the period 1970 to 1990. However

although acceptable at the time, the study did not make use of adequate time series estimation

techniques therefore casting doubt on the estimated results.

Perraton (2003), using data for the 1973 to 1995 period, applied more appropriate estimation

techniques to test the relevance of the balance of payments constrained growth model for a

group of developing countries however, relatively few African countries were included in the

analysis; 12 and 7 for the weak and strong form of Thirlwall’s law respectively. In addition,

both Hussain (1999) and Perraton (2003) did not accommodate for sustainable debt

accumulation and interest rate payments abroad. According to Perraton (2003) it was

“impossible” to measure the growth rate of net capital flows into a country as they fluctuated

between deficit and surplus over the period considered. Moreno-Brid (2003) has theoretically

and empirically shown that sustainable debt accumulation can be incorporated into the model

1 See McCombie and Thirlwall (2004) for a survey of the literature up to 2003.

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by imposing a long term constraint where the ratio of the current account deficit to income is

measured as a constant taken at the beginning of the period.

An empirical study of the balance of payments constrained growth for the sub-Saharan African

region which incorporates sustainable debt accumulation, interest rate payments and the terms

of trade is necessary, as 33 of the 39 countries described as Heavily Indebted Poor Countries

(HIPC) are in sub-Saharan Africa (World Bank, 2015). In addition, majority of the countries

depend on production of primary products in international markets making the terms of trade

effects more pronounced. A study that uses the above extended version of the model, applying

recent data and more appropriate econometric techniques is therefore warranted.

Section 2 is a brief overview of the empirical literature on the balance of payments constrained

growth model. Section 3 outlines the data and methodology used to estimate the model for the

region. Due to uncertainty regarding the stationarity of the variables as a result of structural

breaks in the data, we apply an Autoregressive Distributive Lag (ARDL) model. The results

obtained from estimating the import and export demand functions as well as the estimated

balance of payments constrained growth model are given in section 4.

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2. Literature Review

Thirlwall (1979) developed a post-Keynesian long run growth model, which gives a central

role to demand, using Harrod’s (1933) foreign trade multiplier. Thirlwall (2013) argues that

for most countries demand constraints operate long before supply constraints take effect. The

original Thirlwall (1979) model to estimate the balance of payments constrained growth rate

starts with the balance of payments equilibrium condition,

𝑃𝑑𝑋 = 𝑃𝑓𝑀𝐸 (Equation 2.1)

where Pd is the price of exports in the domestic currency, X is the volume of exports, Pf is the

price of imports in foreign currency, M is the volume of imports and E is the exchange rate

measured as the domestic price of foreign currency.

Taking the logarithms and differentiating with respect to time Equation 2.1 gives,

𝑝𝑑 + 𝑥 = 𝑝𝑓 + 𝑚 + 𝑒 (Equation 2.2)

Where the small case letter x is the growth rate of exports, m is the growth rate of imports, e is

the growth rate of the exchange rate, pd is the growth rate of domestic prices and pf is the growth

rate of import prices.

The import and export demand functions with constant elasticities are as follows:

𝑀 = 𝑎 (𝑃𝑓𝐸

𝑃𝑑) 𝜓 𝑌𝜋 (Equation 2.3)

𝑋 = 𝑏 (𝑃𝑑

𝑃𝑓𝐸) 𝜂 𝑍𝜀 (Equation 2.4)

where a and b are constants, Y is domestic income, Z is the level of world income, 𝜓 is the

price elasticity of demand for imports, 𝜂 is the price elasticity of demand for exports, 𝜋 is

income elasticity of demand for imports and 휀 is the income elasticity of demand for exports.

Taking the logarithms of Equations 2.3 and 2.4 and differentiating with respect to time,

𝑚 = 𝜓(𝑝𝑓 + 𝑒 − 𝑝𝑑) + 𝜋𝑦 (Equation 2.5)

𝑥 = 𝜂(𝑝𝑑 − 𝑒 − 𝑝𝑓) + 휀𝑧 (Equation 2.6)

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where m is the growth rate of imports, pf is the growth rate of foreign prices, e is the growth

rate of the exchange rate, pd is the growth rate of domestic prices, y is the growth rate of

domestic income, x is the growth rate of exports, and z is the growth rate of world income.

Equation 2.5 and 2.6 are then substituted into Equation 2.2 giving,

𝑝𝑑 + (𝜂(𝑝𝑑 − 𝑒 − 𝑝𝑓) + 휀𝑧) = 𝑝𝑓 + (𝜓(𝑝𝑓 + 𝑒 − 𝑝𝑑) + 𝜋𝑦) + 𝑒 (Equation 2.7)

Solving for the growth of income gives the balance of payments constrained growth rate **yB,

∗∗ 𝑦𝐵 = [(1 + 𝜂 + 𝜓)(𝑝𝑑 − 𝑝𝑓 − 𝑒) + 휀𝑧]/𝜋 (Equation 2.8)

Under the assumption that the sum of the price elasticities (+) is equal to unity in absolute

values, and/or if relative prices in international trade, i.e. the real exchange rates are constant,

then Equation 2.8 reduces to,

∗ 𝑦𝐵 = 휀𝑧/𝜋 (Equation 2.9)

where the balance of payments constrained growth rate *yB, is equal to the income elasticity of

demand for exports multiplied by the growth in world income, 휀𝑧, divided by the income

elasticity of demand for imports, 𝜋. Based on the same assumption of constant relative prices,

Equation 2.9 can further be reduced to,

𝑦𝐵 = 𝑥/𝜋 (Equation 2.10)

where the balance of payments constrained growth yB, is equal to the growth in exports x,

divided by the income elasticity of demand for imports, 𝜋. Perraton (2003) described Equation

2.9 as the strong version of Thirlwall’s law as both the import and export demand functions

need to be estimated while Equation 2.10, was recognised as the weak version, as only the

import demand function is needed to derive the balance of payments constrained growth rate.

Equation 2.10 can also be interpreted as the dynamic Harrod (1933) trade multiplier result2.

2 The static Harrod trade multiplier result, Y=X/m where Y is the level of income, X is the level of exports and

m is the marginal propensity to import and 1/m is the foreign trade multiplier. The weak version of the balance

of payments constrained growth can be seen as the dynamic Harrod trade multiplier result, x/ (Thirlwall,

2011).

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The original model described above was extended to include capital flows and terms of trade

(Hussain and Thirlwall, 1982). The extension is particularly relevant for developing countries,

where capital flows, changes in the terms of trade and the real exchange rate have been very

important. An outline of the model can be seen in Appendix A.

The extended model with capital flows and the terms of trade was first empirically tested by

Hussain and Thirlwall (1982) for 20 developing countries covering the 1951 to 1969 period.

Just three sub-Saharan African countries were included in the study: Kenya, Sudan and Zaire3.

The weak version of Thirlwall’s law as given in Equation 2.10, as well as an extended model

which incorporates growth in real capital flows and the terms of trade effects was used. Their

results showed that the countries in the sample had a “very mixed” experience, however on

balance, changes in the terms of trade constrained growth by 0.6% per annum while capital

inflows relaxed the balance of payments constraint and allowed countries to grow faster by

about 0.05% per annum.

The researchers also divided the sample of countries into two sub-groups, the first consisting

of those countries where the balance of payments constrained growth model given in Equation

2.10 under predicted the actual growth rate, y>yB, and those where it over predicted the growth

rate y<yB. As expected, in the first group where y>yB, the rate of growth of real capital inflows

was greater than the growth of exports therefore contributing to the positive difference. For the

countries where y<yB, the rate of growth of capital flows was below the rate of growth of

exports for the majority of the countries in the group; however the dominant constraint to

growth was the adverse effects of relative price movements.

Hussain (1999), tested the weak version of Thirlwall’s law, extending the model to account for

capital flows and the terms of trade as outlined in Hussain and Thirlwall (1982), for 29 African

and 11 Asian economies covering the 1970 to 1990 period. His results for the group of African

3 Zaire is now known as the Democratic Republic of Congo.

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and Asian countries, when tested separately, provided evidence that both the original weak

version and the extended model were good predictors of actual growth. However when the

country groups were combined, the extended model was “superior” to the original model. For

the entire sample of 40 countries, the original model gave valid predictions for 55% of cases

while the extended model faired at 73%. Hussain (1999) therefore concludes that the extended

model developed by Hussain and Thirlwall (1982), is the most appropriate model for sub-

Saharan Africa. One of the limitations of the study is that Ordinary Least Squares (OLS) was

used to estimate the import demand functions for each country without pre testing the

stationarity of the data. The results obtained may therefore be spurious.

Due to the tendency of the Hussain and Thirlwall (1982) model to over predict the rate of

growth, the model was extended by Elliott and Rhodd (1999, p.1146) to include interest rate

payments for, “demand financed by capital flows generally carries with it debt accumulation

and servicing.” Drawing from the sample of countries employed in the Hussain and Thirlwall

(1982) study and extending the model to include external debt financing, Elliott and Rhodd

(1999) were able to reduce the degree of over prediction for 9 out of 13 countries, concluding

that economic growth is additionally constrained by debt service payments which drain on the

limited financial resources needed for economic growth.

The extended balance of payments constrained growth rate developed by Hussain and Thirlwall

(1982) and later modified by Elliott and Rhodd (1999) was further criticised by Moreno-Brid

(1999) as the models did not set a limit to the amount of capital flows into a country and

therefore assumed that a country can forever increase its level of indebtedness relative to Gross

Domestic Product (GDP). In practice, a developing countries creditworthiness and therefore

access to global financial markets is influenced by its debt accumulation as perceived by the

creditors as the current account to GDP ratio and the foreign debt to GDP ratio. As these ratios

increase and reach critical levels, developing countries may experience difficulties in attracting

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foreign capital. This was seen in the 1980’s debt crisis which affected many developing

countries including Latin America and sub-Saharan Africa (Devlin and Ffrench-Davis, 1995).

Sustainable debt accumulation is incorporated into the model by imposing a long run constraint

taken as a constant ratio of the current account deficit to income (Moreno-Brid, 2003). This

version of the model which accounts for sustainable debt accumulation, interest rate payments

and the terms of trade has not been tested for the sub-Saharan African region. It has however

been tested by Moreno-Brid (2003) for Mexico4, with the results providing support for the

balance of payments constrained growth model as well as the importance of interest rate

payments as an additional binding constraint to Mexico’s growth rate.

Other extensions of the model include Nell (2003) and Lanzafame (2014). Nell (2003)

generalised the balance of payments constrained growth model to include many countries. He

was therefore able to analyse South Africa’s balance of payments constraint with respect to the

OECD and the rest of the Southern African Development Community (RSADC). The results

showed that South Africa was only balance of payments constrained with respect to the OECD

and faster growth rates may be the result of an improvement in the structural demand feature

of its exports to the OECD.

Lanzafame (2014) synthesised the two growth literatures on the Harrod (1939) natural rate of

growth and the balance of payments constrained growth model. Using 22 OECD countries for

the 1960 to 2010 period, he provided evidence that the natural rate of growth was equal to the

balance of payments constrained rate of growth. Applying Granger-causality tests, he provided

further evidence that there was unidirectional long run causality from the balance of payments

constrained growth to the natural rate of growth, therefore reinforcing the view that long run

growth is demand determined and constrained by the balance of payments.

4 The model empirically tested by Moreno-Brid (2003) assumed that the terms of trade are constant.

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3. Data and Methodology

There have been several extensions to the original balance of payments constrained growth

model. The chosen model for the sub-Sahara African region is the one modified by Moreno-

Brid (2003) which allows for sustainable debt accumulation, interest rate payments and the

terms of trade. As far as we are aware, there are no current papers which test this version of the

model for the region. Below is an outline of the data, model and the methodology used to

estimate and test the balance of payments constrained growth model.

3.1 Data

Data covering the 1960 to 2014 period is used in the analysis. The time period used differs for

individual countries due to data availability. The variables used are exports of goods and

services, imports of goods and services, Gross Domestic Product (GDP), world income, import

price index, export price index, interest payments on external debt and the real effective

exchange rate. Please see Appendix B for a full description of the data and sources used.

3.2 The Model

In line with Hussain and Thirlwall (1982), Moreno-Brid (2003) and Thirlwall (2012), the

starting point of the extended model of the balance of payments constrained growth model is

the balance of payments accounting identity in disequilibrium which will be modified

accordingly to accommodate for sustainable debt accumulation, interest rate payments and the

terms of trade.

𝑃𝑑𝑋 + 𝐹𝑃𝑑 = 𝑃𝑓𝑀𝐸 (Equation 3.1)

Where, Pd, is the price of exports in the domestic currency, X, is the volume of exports, F is the

current account deficit in real terms so that FPd, is nominal capital flows to finance the deficit,

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Pf, is the price of imports in foreign currency, M, is the volume of imports and E, is the exchange

rate measured as the domestic price of foreign currency5.

Taking the first difference of the variables in logarithmic form yields,

𝜃(𝑝𝑑 + 𝑥) + (1 − 𝜃)(𝑓 + 𝑃𝑑) = 𝑝𝑓 + 𝑚 + 𝑒 (Equation 3.2)

Where, 𝜃, and (1-𝜃), represent the share of exports and capital flows as a proportion of total

receipts respectively. Therefore 𝜃 = 𝑃𝑑𝑋/𝑅 and (1 − 𝜃) = 𝐹𝑃𝑑/𝑅, where R is total receipts

which can also be expressed as the import bill financed by export earnings and capital flows.

Lower case letters denote growth rates.

Equation 3.2 is modified to include sustainable debt accumulation and interest rate payments

abroad (Moreno-Brid, 2003). We account for interest payments abroad by subtracting interest

payments from capital flows,

𝜃(𝑝𝑑 + 𝑥) − 𝜃1(𝑝𝑑 + 𝑟) + (1 − 𝜃 + 𝜃1)(𝑓 + 𝑃𝑑) = 𝑝𝑓 + 𝑚 + 𝑒 (Equation 3.3)

Where, r, is the growth rate of real net interest payments abroad and, θ1, is the share of foreign

exchange used for interest payments abroad. Corresponding to sustainable debt accumulation

in the long run, we assume that the current account deficit to GDP ratio is constant, hence we

set f=y6. Substituting the growth of imports and exports from Equations 2.5 and 2.6, setting

f=y and solving for the growth of income7,

𝑦𝐵𝑆𝐷𝐴𝑅𝑇 =𝜃𝜀𝑧−𝜃1𝑟+(𝜃𝜂+𝜓+1)(𝑝𝑑−𝑝𝑓−𝑒)

𝜋−(1−𝜃+𝜃1) (Equation 3.4)

where yBSDART, is the balance of payments constrained growth rate with sustainable debt

accumulation, interest rate payments abroad and the terms of trade.

5 For simplicity the nominal exchange rate is assumed to be fixed and equal to one (Moreno-Brid, 2003). 6 Following Moreno-Brid (2003), we set the growth in capital flows equal to the growth in income,

𝑑𝑓

𝑓=

𝑑𝑦

𝑦.

7 Substituting the import and export demand functions in Equation 3.3 yields, 𝜃 (𝑝𝑑 + (𝜂 (𝑝𝑑−𝑒−𝑝𝑓) + 휀𝑧)) −

𝜃1(𝑝𝑑 + 𝑟) + (1 − 𝜃 + 𝜃1)(𝑓 + 𝑃𝑑) = 𝑝𝑓 + (𝜓(𝑝𝑓 + 𝑒 − 𝑝𝑑) + 𝜋𝑦) + 𝑒.

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Under the assumption of constant relative prices8, Equation 3.4 reduces to,

∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 =𝜃𝑥−𝜃1𝑟+(𝜓+1)(𝑝𝑑−𝑝𝑓−𝑒)


If the terms of trade are neutral and the Marshall Lerner condition is met, i.e. 𝜓 = −1 then

Equation 3.5 reduces to,

𝑦𝐵𝑆𝐷𝐴𝑅 =𝜃𝑥−𝜃1𝑟


Where, 𝑦𝐵𝑆𝐷𝐴𝑅, is the balance of payments constrained growth rate with sustainable debt

accumulation and interest payments abroad. If there are no interest payments, hence θ1=0, then

Equation 3.6 becomes,

𝑦𝐵𝑆𝐷𝐴 =𝜃𝑥

𝜋−(1−𝜃) (Equation 3.7)

Where, 𝑦𝐵𝑆𝐷𝐴, is the balance of payments constrained growth rate with sustainable debt

accumulation. If a country does not have a deficit then θ=1, and Equation 3.7 reduces to the

weak form of Thirlwall’s original law,

𝑦𝐵 = 𝑥/𝜋 (Equation 2.10)

When comparing the different models of the balance of payments constraint growth rate we

expect,

the balance of payments constrained growth rate with capital flows to be higher than

the original model as we assume the countries under consideration to be net borrowers

and hence capital inflows relax the balance of payments constraint.

the terms of trade effect to be either negative or positive depending on the experience

of the country in question.

8 This specification, ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 =

𝜃𝑥−𝜃1𝑟+(𝜓+1)(𝑝𝑑−𝑝𝑓−𝑒)

𝜋−(1−𝜃+𝜃1), does not include estimates from the export demand

function, i.e. the income elasticity of demand or the price elasticity of demand for exports.

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the balance of payments constraint growth model with sustainable debt accumulation

and interest rate payments to be lower than the model that does not set a limit to capital

inflows or account for interest rate payments abroad9.

3.2.1 Economic Propositions

The higher the income elasticity of demand for imports 𝜋, the lower the balance of payments

constrained growth rate. A faster growth rate of world income z, will raise the balance of

payments constrained growth rate.

Furthermore, the Marshall-Lerner condition is assumed to be true. That is, devaluations or a

currency depreciation measured by the increase in the domestic price of foreign currency (e>0),

will improve the balance of payments constrained growth rate provided that the absolute value

of the sum of the price elasticity of demand for exports weighted by the proportion of the total

import bill financed by export earnings and the price elasticity of demand for imports is greater

than unity, i.e. |𝜃𝜂 + 𝜓| > 1. However, even if the condition (|𝜃𝜂 + 𝜓| > 1) is satisfied, a once

off devaluation will not raise the balance of payments constrained growth rate permanently.

After an initial devaluation, e, will fall back to zero and the growth rate will backslide to its

former level (Hussain and Thirlwall, 1982).

3.3 Estimation Methodology

The estimation methodology is outlined below, this includes the unit root tests used to test the

stationarity of the data, the Autoregressive Distributive Lag (ARDL) model and the bounds

testing procedure used to test for cointegration.

9 We do not estimate the balance of payments constrained growth model with unlimited capital flows as it is not

necessary to include this specification of the model in order to obtain the balance of payments constrained

growth rate with sustainable debt accumulation. In addition there is a lack of comparable data across countries

on capital flows.

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3.3.1 Unit Root tests and Structural Breaks

The sub-Saharan African countries have experienced several shocks over the last five decades.

It is therefore necessary to account for structural breaks when testing the stationarity of the

data. In this case the typical Augmented Dickey Fuller (ADF) test and the Phillips Perron (PP)

test, whose null hypothesis is, there is a unit root may be invalid as the tests are biased towards

the non-rejection of the hypothesis in the presence of a structural break, finding a unit root

when it may actually not exist (Perron, 1989). In addition, Clemente et al (1998) have provided

empirical evidence that it is erroneous to account for one structural break if in fact the series

contains more breaks. Our preferred unit root test is therefore the Clemente, Montanes and

Reyes (CMR) test which allows for two endogenously determined structural breaks. It is a

modification of the Perron and Vogelsang (1992) unit root test which accounts for one break

in the series. If evidence of only one structural break is found in the series then the Perron and

Vogelsang test will be used. If there is no evidence of any structural break in the series then

the traditional ADF and PP unit root tests will be used.

The Clemente, Montanes and Reyes unit root test allows for two different types of structural

breaks. Sudden changes in the series are captured by the Additive Outliers (AO) model while

a gradual shift in the mean of the series is detected by the Innovational Outliers (IO) model

(Baum, 2005). Both forms of structural change will be tested.

The null hypothesis is that the series has a unit root with a structural break while the alternative

hypothesis is that the series is stationary with breaks. Prior knowledge of the structural break

date or appropriate lag order is not needed as they are determined by a two dimensional grid

search which looks for the lowest possible value for the t statistic from all the possible break

points; allowing for the “strongest rejection” of the null hypothesis. A set of sequential F tests

determines the lag order (Baum, 2005).

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Endogenously determining the structural break is preferred to exogenously determining it as

the latter is considered to be identified ex ante which is inappropriate as it invalidates the

distribution theory underlying conventional testing (Christiano, 1992).

Structural breaks in the data will be addressed during estimation through the use of dummy

variables. Including dummy variables to account for structural breaks is more efficient than

splitting the sample, particularly when the sample size is relatively small (McCombie, 1997).

Only significant dummy variables will be retained in the model.

3.3.2 Autoregressive Distributive Lag (ARDL) Model

The presence of structural breaks in the data creates uncertainty as to the stationarity of the

variables. An ARDL model will therefore be used to estimate the import and export demand

functions needed to calculate the balance of payments constrained growth rate. One advantage

of the ARDL model is that it provides consistent estimates irrespective of whether the variables

are integrated of order one (I(1)), or zero I(0) (Pesaran and Shin, 1998). The purpose of the unit

root tests are to ensure that none of the series included are I(2), as this would invalidate the

methodology.

The ARDL model is preferred to the Vector Autoregressive (VAR) model as it utilises a single

equation estimation technique, making interpretation relatively simple. Another advantage

when using the ARDL model is the lag order of the dependent and independent variables are

allowed to vary without affecting the asymptotic result.

In addition, it is possible to test for cointegration using the bounds testing procedure. Other

cointegration tests such as the Johansen system-based reduced rank regression approach or the

Engle-Granger two step residual-based procedure, are restricted to only I(1) variables. Pesaran

and Shin (1998), further show that the bounds cointegration test is superior to the Johansen

cointegration test in small samples.

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A general ARDL(p,q) is outlined below,

𝑦𝑡 = 𝛼0 + 𝛼1𝑡 + ∑ ∅𝑖𝑦𝑡−𝑖𝑝𝑖=1 + 𝛽′𝑥𝑡 + ∑ 𝛽𝑖

∗′𝑞−1𝑖=0 ∆𝑥𝑡−𝑖 + 𝑢𝑡

∆𝑥𝑡 = 𝑃1∆𝑥𝑡−1 + 𝑃2∆𝑥𝑡−2 + ⋯ + 𝑃𝑠∆𝑥𝑡−𝑠 + 휀𝑡 (Equation 4.1)

Here the underlying variables are I(1) however the model provides consistent results even when

modified to include a mixture of I(1) and I(0) variables or just I(0) variables. The dependent

variable yt, is regressed on its lagged values yt-1, a set of dependent I(1) xt, variables that are

not cointegrated amongst themselves, and the differenced lagged variables of xt. Ut, and εt, are

serially uncorrelated disturbances with the usual mean of 0 and constant variance and

covariance. Correlation between ut, and εt, can be overcome by including an adequate number

of lagged changes in the regressors. Pi, are the k x k coefficient matrices so that the vector

autoregressive process in ∆xt, is stable10. Two additional assumptions are made, that the roots

of, 1 − ∑ ∅𝑖𝑧𝑖 = 0𝑝

𝑖−1 , all fall outside the unit circle and a long run stable relationship exists

between yt, and xt (Pesaran and Shin, 1998) 11.

The contemporaneous dependence between ut, and εt, is explicitly modelled in order to derive

the short run effects. Pesaran and Shin (1998) have shown that the ARDL approach to

estimation and inference is asymptotically valid.

The ARDL model outlined above can be reparametrized in the form of an error correction (EC)

model (Hassler and Wolters, 2005),

∆𝑦𝑡 = 𝑐0 + 𝑐1𝑡 + 𝛾𝑦𝑡−1 + 𝜗′𝑥𝑡−1 + ∑ 𝑎𝑖∆𝑦𝑡−𝑖𝑝−1𝑖=1 + ∑ 𝛽𝑖

′𝑛−1𝑖=0 ∆𝑥𝑡−𝑖 + 𝑢𝑡 (Equation 4.2)

Where, γ = -a(1), ϑ = a(1)β = -γβ.

The above model contains both an intercept and trend however it can be expressed as having

just an intercept or neither an intercept and trend.

10 Xt is the k-dimensional I(1) variables. 11 Under this assumption, the elements of zt, are allowed to be purely I(1), purely I(0) or cointegrated. The

possibility of seasonal unit roots and explosive roots are excluded (Pesaran et al 2001).

15

When using the ARDL model, selecting the right lag order is important for valid inferences.

The appropriate lag order will be selected using the Schwarz Bayesian Criterion (SBC) as

according to Pesaran and Shin (1998), the ARDL model using the SBC performed slightly

better than the ARDL model using the Akaike Information Criterion (AIC). This may be

because SBC is a consistent model selection criterion while the AIC is not.

The usual normality tests will be carried out to ensure appropriate model selection. This

includes the Breusch-Pagan/Cook-Weisberg test for heteroscedasticity and the Breusch-

Godfrey test for serial correlation. The stability of the model over time is tested by calculating

and graphing the cumulative sums (CUSUM) as well as the CUSUM squared of the recursive

residuals from the variables defined in the model and their respective 95% confidence bands.

Following the selection of the appropriate ARDL model, the long run parameters and valid

standard errors need to be obtained12. The latter will be estimated using the Ordinary Least

Squares (OLS) delta method (∆-method)13. This approach is directly comparable to the fully

modified OLS approach of Phillips and Hansen (1990)14, however Pesaran and Shin (1998)

have provided some evidence that the delta method outperforms the latter in small samples.

Additionally, the delta method results are asymptotically valid irrespective of whether xt, is

I(1) or I(0).

The static formulation of the cointegrating regression can be expressed as,

𝑦𝑡 = 𝜇 + 𝛿𝑡 + 𝜃′𝑥𝑡 + 𝑣𝑡

∆𝑥𝑡 = 𝑒𝑡 (Equation 4.3)

12 The ARDL long run variance is defined as, 𝜎𝜂

2/[𝜙(1)]2. 13 The Bewley’s (1979) regression approach is an alternative method for estimating the long run parameters

from the selected ARDL model. It provides identical results to the OLS delta method (Pesaran and Shin, 1998).

Preference is based on computational convenience. 14 Problem with the OLS estimator, the unit root distribution and second order bias arising from the

contemporaneous correlation, which may exist between vt, and et, is generally involved in the asymptotic

distribution of the OLS estimator of the long run parameter θ. As inferences on θ using the t-tests in the OLS

regression are therefore invalid, Phillips and Hansen (1990) suggest the adoption of a fully-modified OLS

procedure. Both the fully-modified OLS procedure and the ARDL based are asymptotically valid. Preference

between the two is based in computational convenience (Pesaran and Shin, 1998).

16

Where δ, and θ, are the long run parameters defined in the level ARDL model in Equation 4.1,

by the ratio δ = 𝛼1/∅(1) , and θ = β/∅(1), where ∅(1) = 1 − ∑ ∅𝑖𝑝𝑖=1 . From the error

correction or first differenced ARDL model in Equation 4.2, the long run parameters δ, and θ,

are defined as, 𝛿 = −𝑐1/𝛾, and, 𝜃 = −𝜗/𝛾. The long run parameters estimated from the level

form and the first difference form are identical (Hassler and Wolters, 2005). We therefore make

use of the conditional error correction ARDL model as the existence of a single long run level

relationship between the levels of yt, and xt, can easily be tested using the bounds testing

procedure.

From the estimated error correction model in Equation 4.2, we can use the Wald or F statistic

to test the joint hypothesis that there is no level relationship between the level variables yt and

xt, i.e. H0: γ=0 and ϑ=0’. Pesaran et al (2001), provide two sets of critical value bounds covering

all possible classifications of the forcing variable {xt}, into I(0) which provides the lower

bound, I(1) related to the upper bound and mutually integrated process15. A conclusive decision

regarding cointegration of the variables can be made when the computed F statistic falls outside

the critical value bounds. If the computed F statistic is greater than the upper bound critical

value, then the null hypothesis of no single long run relationship between the variables is

rejected. If the computed Wald or F statistic is below the lower bound critical value, we accept

the null hypothesis of no long run level relationship between the variables. If however the

computed Wald or F statistic falls within the bounds, inference would be inconclusive and the

rank, r, of the forcing variables {xt}, would need to be determined in order to proceed.

In the absence of cointegration, we take the first difference of the variables and estimate the

import and export demand function using OLS.

15 The asymptotic critical values are obtained through simulation for when, 𝑟 =𝑘 and {𝑥𝑡}~(1) and also for when 𝑟 = 0 and {𝑥𝑡}~(1). R, the cointegration rank of the forcing variables {xt}

follows the process 0 ≤ r ≤ k (Pesaran et al, 2001).

17

3.4 Testing the Balance of Payments Constrained Growth Model

Several procedures have been proposed for testing the equivalence of the balance of payments

constrained growth rate to the actual growth rate of a country16. An informal method is to look

at the estimated export demand function. If the income elasticity of demand for exports, 휀,̂ is

statistically significant and the coefficient on the relative price index, 𝜂,̂ is small and

insignificant, we cannot refute the balance of payments constrained growth (Britto and

McCombie, 2009).

We make use of two formal approaches. The first approach allows us to formally test the

balance of payments constrained growth model for an individual country while the second

approach allows us to test the model for a group of countries. For the first approach, we make

use of the method proposed by McCombie (1989) which is to calculate the hypothetical income

elasticity of demand which exactly equates the actual rate of growth using the balance of

payments constrained model. We then test if it is equal to the estimated income elasticity of

demand from the import demand function using the Wald test. Failing to reject the null

hypothesis for the equivalence between the two elasticities of demand would provide evidence

in favour of the balance of payments constrained growth rate.

Due to variations in the export to import ratio, θ, and the interest payment to import ratio, θ1,

we calculate the hypothetical growth rate using both the start value at the beginning of the

period concerned and the average value for the period (Britto and McCombie, 2009). The

hypothetical income elasticities that would equate the actual rate of growth given by the

balance of payments constrained growth model are shown in Table 1.

16 For a full outline of all the different methods proposed see McCombie (1997).

18

Table 1; Hypothetical income elasticity of demand for imports, 𝜋𝐻 (Moreno-Brid, 2003)

Balance of payments constrained growth model Solving for the income elasticity of demand

∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 =𝜃𝜖𝑧 − 𝜃1𝑟 + (𝜃𝜂 + 𝜓 + 1)(𝑝𝑑 − 𝑝𝑓 − 𝑒)

𝜋 − (1 − 𝜃 + 𝜃1) ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 = (1 − 𝜃 + 𝜃1) +

𝜃𝜖𝑧 − 𝜃1𝑟 + (𝜃𝜂 + 𝜓 + 1)(𝑝𝑑 − 𝑝𝑓 − 𝑒)

𝑦

𝑦𝐵𝑆𝐷𝐴𝑅𝑇 =𝜃𝑥 − 𝜃1𝑟 + (𝜓 + 1)(𝑝𝑑 − 𝑝𝑓 − 𝑒)

𝜋 − (1 − 𝜃 + 𝜃1)

𝜋𝐻𝐵𝑆𝐴𝐷𝑅𝑇 = (1 − 𝜃 + 𝜃1) +𝜃𝑥 − 𝜃1𝑟 + (𝜓 + 1)(𝑝𝑑 − 𝑝𝑓 − 𝑒)

𝑦

𝑦𝐵𝑆𝐷𝐴𝑅 =𝜃𝑥 − 𝜃1𝑟

𝜋 − (1 − 𝜃 + 𝜃1)

𝜋𝐻𝐵𝑆𝐷𝐴𝑅 = (1 − 𝜃 + 𝜃1) +𝜃𝑥 − 𝜃1𝑟

𝑦

𝑦𝐵𝑆𝐷𝐴 =𝜃𝑥

𝜋 − (1 − 𝜃)

𝜋𝐻𝐵𝑆𝐷𝐴 = (1 − 𝜃) +𝜃𝑥

𝑦

𝑦𝐵 =𝑥

𝜋

𝜋𝐻𝐵 =𝑥

𝑦

Note: ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments abroad and the terms of trade interacted with the price elasticities of

demand for imports and exports

𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments and the terms of trade (only the income and price elasticities from the import

demand function are included)

𝑦𝐵𝑆𝐷𝐴𝑅, is the balance of payments constrained growth with sustainable debt accumulation and interest payments abroad

𝑦𝐵𝑆𝐷𝐴, is the balance of payments constrained growth with sustainable debt accumulation

𝑦𝐵, is the ‘weak’ original version of the balance of payments constrained growth model

19

Our second approach was first proposed by McGregor and Swales (1985) and later modified

by McCombie (1997), makes use of pooled data for all the countries. McGregor and Swales

(1985) regress the actual rate of growth on the balance of payments constrained growth and

test the hypothesis that the intercept and slope coefficient are not statistically different from 0

and 1 respectively. As pointed out by McCombie (1997, p.347), the above regression suffers

from a, “misspecification analogous to an error in variables problem,” as the balance of

payments constrained growth rates are stochastic as they were derived from prior estimation

coefficients which have associated standard errors. A simple way to overcome this is to regress

the balance of payments constrained growth rate on the actual growth rate17. The modified

method proposed by McCombie (1997) will be applied. One of the limitations of this approach

is that countries that persistently run a balance of payments surplus must be excluded from the

regression. According to McCombie (1997), this does not invalidate the balance of payments

constrained model as not all countries can be balance of payments constrained. In this case, we

are testing that the sub-Saharan African countries are balance of payments constrained.

4. Results

The results obtained from the unit root tests, the estimated import and export demand functions

using the ARDL model and the estimates for the balance of payments constrained growth

model are presented in this section.

4.1 Unit Root Tests

The results from the unit root tests can be seen in Appendix C. All the variables were either

I(0) or I(1) as determined by the Augmented Dickey Fuller (ADF) test, the Phillips Perron (PP)

test, the Perron and Vogelsang test and the Clemente, Montanes and Reyes (CMR) test. The

17 The decision to regress the balance of payments constrained growth on the actual rate of growth does not

indicate causality (McCombie, 1997).

20

appropriate unit root test was chosen based on the presence of no structural break, one structural

break or two structural breaks respectively. As all the variables are either I(0) or I(1) we

proceed with the ARDL model to estimate the import and export demand functions.

4.2 Import Demand Function

The import demand function is estimated for 22 sub-Saharan African countries. The summary

of results derived using the ARDL model can be seen in Table 2. Only the long run estimates

for the income elasticity of demand and the price elasticity of demand for imports along with

some of the diagnostic tests are reported. Appendix D contains more detailed results, including

the short run estimates. Appendix J contains the CUSUM and CUSUM squared graphs which

test the stability of the model.

For 13 countries, the price elasticity of demand for imports was small and insignificant, ranging

from -1.494 for Kenya to -0.121 for Uganda, highlighting the small role relative prices have

played in the region. The income elasticity of demand for imports was significant for 20

countries. For Zambia, the income elasticity of demand for imports was 4.562 which is

relatively high as the income elasticity of demand for imports for the rest of the 19 countries

ranged from 0.475 for Gambia to 2.310 for Sierra Leone. This provides evidence in favour of

the balance of payments constrained growth rate as it shows that relative prices play a very

small or no role in the import demand function. What is of importance is the income elasticity

of demand for imports which is determined by a countries economic structure.

For Gabon, Democratic Republic of Congo, Mali, Sierra Leone, Sudan and Uganda we do not

find any evidence against the null hypothesis of no cointegration between the variables using

the bounds testing procedure. We therefore take the first difference of the variables and re-

estimate the import demand function using OLS. We follow the same procedure for Togo as

we could not estimate a stable import demand function using the ARDL model. A summary of

the results can be seen in Table 3.

21

Table 2; Summary of the long run estimates from the import demand function estimated using the ARDL model

The income

elasticity of

demand for

imports, π

The price

elasticity of

demand for

imports, ψ ARDL SBC R2

Bounds F

test

Breusch-

Pagan/Cook-

Weisberg test for

heteroscedasticity

(P value)

Breusch-

Godfrey test

for serial

correlation

(P value)

Benin 1.142*** (0.109) -1.08*** (0.242) (1 1 1) -74.481 0.795 10.289*** 0.997 0.508

Botswana 0.896*** (0.023) -0.53*** (0.168) (3 1 0) -67.41 0.756 10.200*** 0.471 0.744

Cameroon 1.379*** (0.087) 0.657*** (0.177) (1 0 0) -63.204 0.403 5.775** 0.639 0.664

Chad 0.659*** (0.157) -0.278* (0.152) (2 0 0) -21.17 0.852 20.472*** 0.163 0.681

Congo, Dem. Rep.18 2.179* (1.266) -0.278 (0.546) (2 1 1) -12.424AIC 0.568 3.754 0.772 0.193

Congo, Rep. 1.483*** (0.291) -1.036 (0.627) (3 3 3) -57.642 0.968 4.221* 0.493 0.293

Gabon 1.275*** (0.155) -0.85*** (0.226) (1 1 0) -57.804 0.659 3.182 0.257 0.751

Gambia 0.475** (0.193) -0.25 (0.243) (2 1 1) -63.965AIC 0.44 4.212* 0.67 0.346

Kenya 0.986*** (0.212) -1.494*** (0.354) (1 0 0) -58.354 0.272 3.892* 0.119 0.644

Mali 2.195** (1.07) -0.64 (2.089) (1 1 1) -35.912 0.179 0.716 0.136 0.156

Mauritius 1.183*** (0.165) -1.131 (1.537) (1 2 4) -83.903 0.86 5.404** 0.893 0.095*

Mozambique 1.877*** (0.451) -0.168** (0.064) (1 2 1) -50.439 0.696 9.674*** 0.535 0.562

Namibia 1.946*** (0.184) -0.148 (0.615) (1 2 2) -64.769 0.786 5.280** 0.829 0.817

Nigeria 0.941*** (0.299) -0.148 (0.109) (1 3 1) -6.661 0.872 9.114*** 0.238 0.135

Senegal 1.107*** (0.081) -0.126 (0.126) (1 0 0) -97.159 0.491 6.911*** 0.515 0.452

Sierra Leone 2.310** (0.977) 0.68 (0.802) (1 1 1) -3.750AIC 0.363 2.87 0.039** 0.843

South Africa19 0.819 (0.59) -1.064 (0.399) (1 1 0) -131.366 0.803 10.590*** 0.776 0.263

Sudan 0.957*** (0.197) 0.177 (0.309) (1 0 0) -1.585 0.147 2.657 0.743 0.802

Uganda 1.553*** (0.236) -0.121 (0.157) (4 4 3) -83.982 0.953 2.751 0.435 0.886

Zambia 4.562* (2.169) -0.267 (0.199) (1 4 5) -18.215 0.841 4.912** 0.364 0.953

Zimbabwe 1.167*** (0.237) -0.281* (0.146) (1 0 1) -19.28 0.695 9.487*** 0.008*** 0.938 Note: AIC indicates that the model was selected using the AIC criterion due to the persistence of autocorrelation when using the model selected by SBC

Standard errors are in parenthesis

*** Indicates significance at the 99% level

** Indicates significance at the 95% level

* Indicates significance at the 90% level

18 For the Democratic Republic of Congo we control for the ongoing civil war which started in 1997 till present. 19 A trend is added for South Africa. We control for apartheid which made very little difference to the outcome. The results can be seen in Appendix F.

22

Table 3; Summary of results for the import demand function estimated using OLS

Country

The

income

elasticity

of

demand

for

imports, π

The price

elasticity

of

demand

for

imports,

ψ R2

Breusch-

Pagan/Cook-

Weisberg

test for

heteroscedas-

ticity

(P value)

Breusch-

Godfrey test

for serial

correlation

(P value)

Congo,

Dem.Rep.

2.372*** (0.605) -0.053 (0.127) 0.247 0.805 0.524

Gabonrobust 0.979*** (0.284) -0.178 (0.221) 0.579

Mali 0.049 (0.374) -0.099 (0.169) 0.352 0.314 0.197

Togorobust 1.608*** (0.495) -0.834*** (0.203) 0.217

Ugandarobust 2.061*** (0.613) -0.225*** (0.059) 0.557

Sierra Leone 0.775 (0.501) 0.416* (0.216) 0.173 0.323 0.675

Sudan 0.963 (0.562) -0.095 (0.094) 0.070 0.172 0.392 Note: Standard errors are in parenthesis robust are heteroscedasticity consistent standard errors




The income elasticity of demand using OLS for the Democratic Republic of Congo, Gabon,

Uganda and Sudan were close to that estimated using the ARDL model as there was less than

a 0.5 point difference. We therefore proceed to estimate the balance of payments constrained

growth using both the estimates obtained from the ARDL model as well as OLS for the above

mentioned countries.

The income elasticity of demand for imports using OLS ranged from 0.963 for Sudan to 2.372

for the Democratic Republic of Congo. The price elasticity of demand for imports ranged from

-0.834 for Togo to -0.05 for the Democratic Republic of Congo.

It was not possible to estimate reasonable import demand functions using OLS for Mali and

Sierra Leone as the income elasticity of demand for imports was insignificant at the 10% level.

The price elasticity of demand for imports for Mali was insignificant and had the wrong sign

for Sierra Leone. We therefore proceed with the results obtained from the ARDL model for

these two countries although caution is needed when making inferences.

23

4.2.1 Comparing the Estimated Income Elasticity of Demand with those from Other Studies

Due to the importance of the income elasticity of demand for calculating the balance of

payments constrained growth rate, we compare our estimates with those from other studies.

According to McCombie (1997), the income elasticity of demand for imports is stable over

time as it represents non price based competition which changes very slowly. It is therefore

still informative to compare our results with those from other studies in the region despite the

time frame covered being different. The comparison can be seen in Table 4. Our estimates

appear reasonable as they are close to those estimated in other studies. The income elasticity

of demand ranged from 0.34 to 5.0 in other studies (Senhadji, 1998; Hussain, 1999; Perraton,

2003) while it ranged from 0.475 to 4.562 in our analysis.

Table 4; Comparison of the estimated income elastictity of demand with other studies

Country

Our

Estimates

Senhadji

(1998)

Hussain

(1999)

Perraton

(2003)

Benin 1.142 4.91 1.97

Botswana 0.896

Cameroon 1.379 1.01 0.84 0.88

Chad 0.656

Congo Dem. Rep. 2.179

Congo Rep. 1.483 0.87 1.44

Gabon 1.275 1.37

Gabon (OLS) 0.979

Kenya 1.06 1.14 0.98 1.84

Gambia 0.475 1.51

Mali 2.195 0.87

Mauritius 1.183 2.25 1.23 1.17

Mozambique 1.877

Namibia 1.946

Nigeria 0.941 1.81 2.70

Senegal 1.107 2.26 0.98

Sierra Leone 2.310 1.54

South Africa 0.955 0.67 1.38

Sudan 0.957 1.57

Togo 1.608 1.93 5.00

Uganda 1.553

Uganda (OLS) 2.061

Zambia 4.562 0.34 1.11

Zimbabwe 1.167 1.64 Note: OLS indicates the income elasticity of demand from the import demand function using OLS

24

4.3 Export Demand Function

A summary of the results for the export demand function can be seen in Table 5. Only the long

run estimates and the results from the diagnostic tests are shown. For full details of the results

including the short run coefficients please see Appendix E.

We were able to estimate the export demand function for 19 countries using the ARDL model.

The income elasticity of demand for exports ranged from 0.606 for Senegal to 3.446 for Uganda

however it was much higher for Mozambique at 4.786, Zambia at 8.041 and Zimbabwe at

14.607. The price elasticity of demand for exports was less than zero in absolute terms for 12

countries. It was insignificant for 14 countries. For the 5 countries where the price elasticity of

demand for exports was significant at the 5% level, it stood at, -1.577 for Botswana, -0.605 for

the Republic of Congo, -0.860 for Mali, -6.865 for Sudan and -1.390 for Zimbabwe. These

results provide further support for the balance of payments constrained growth model.

For Kenya, Benin, Cameroon, Democratic Republic of Congo, Chad, and Mauritius we fail to

find any evidence of cointegration using the bounds testing procedure. For Gabon, we could

not estimate a stable export demand function with the ARDL model and therefore proceed with

OLS, making the necessary adjustments to account for the non-stationarity of the variables.

25

20 The export demand function for Benin is from 1974-2015 due to data availability.

Table 5; Summary of results for the export demand function estimated using the ARDL model

The income

elasticity of

demand for

exports, ε

The price

elasticity of

demand for

exports, η ARDL SBC R2

Bounds F

test

Breusch-

Pagan/Cook-

Weisberg test for

heteroscedasticity

(P value)

Breusch-

Godfrey test for

serial

correlation

(P value)

Benin20 2.673*** (0.54) 0.058 (0.455) (6 7 6 ) 13.046 0.591 1.927 0.811 0.223

Botswana 1.937*** (0.188) -1.577** (0.689) (1 1 0) -48.83 0.621 3.465 0.225 0.212

Cameroon 1.348*** (0.379) -0.496 (0.749) (1 1 0) -51.295 0.574 2.555 0.373 0.75

Chad 2.469** (0.968) 1.261 (0.896) (1 2 0) 22.52 0.483 2.26 0.045** 0.181

Congo, Dem.

Rep.

2.83 (1.098) 0.74 (0.648) (1 1 1) -9.155 0.407 3.724 0.424 0.278

Congo, Rep. 1.018*** (0.113) -0.605*** (0.125) (1 2 0) -98.318 0.65 6.615*** 0.892 0.158

Gambia 1.198*** (0.247) 0.873 (0.259) (2 1 1) -63.188AIC 0.658 7.447*** 0.282 0.249

Kenya 1.218*** (0.372) -0.425 (1.123) (1 0 1) -103.528 0.197 0.622 0.662 0.162

Mali 1.851*** (0.248) -0.860*** (0.279) (1 0 4) -62.539 0.745 8.413*** 0.852 0.57

Mauritius 1.581*** (0.418) -0.816 (1.652) (1 1 1) -81.53 0.489 0.575 0.034** 0.203

Mozambique 4.786*** (0.44) -0.45 (0.423) (1 0 0) -50.477 0.665 9.997*** 0.239 0.283

Namibia 1.299*** (0.052) 0.187 (0.136) (2 2 2) -68.298 0.753 13.251*** 0.975 0.274

Nigeria 1.668*** (0.263) 0.035 (0.119) (1 0 0) 1.534 0.389 4.366* 0.456 0.347

Senegal 0.606*** (0.089) -0.099 (0.128) (1 3 0) -61.174 0.717 16.575*** 0.040** 0.515

South Africa 1.637** (0.629) 0.268 (0.839) (1 1 1) -175.118 0.598 6.253** 0.095* 0.234

Sudan 0.719 (0.503) -6.865** (2.868) (2 0 3) -22.575 0.565 13.214*** 0.018** 0.598

Uganda 3.466*** (0.586) -0.011 (0.287) (1 1 1) -16.188 0.43 4.599* 0.95 0.201

Zambia 8.041** (3.557) -10.155 (7.02) (2 2 2) -25.404 0.809 11.132*** 0.152 0.599

Zimbabwe 14.607*** (3.615) -1.390*** (0.278) (4 1 4) -36.537 0.806 8.502*** 0.074* 0.331 Note: AIC indicates that the model was selected using the AIC criterion due to the persistence of autocorrelation when using the model selected by SBC





26

Table 6; Summary of results for the export demand function estimated using OLS

Country

The

income

elasticity

of

demand

for

imports, π

The price

elasticity

of

demand

for

imports,

ψ R2

Breusch-

Pagan/Cook-

Weisberg

test for

heteroscedas-

ticity

(P value)

Breusch-

Godfrey

test for

serial

correlation

(P value)

Congo,

Dem. Rep.

3.972** (1.793) -0.066 (0.111) 0.135 0.389 0.522

Gabon 1.781 (0.988) -0.071 (0.201) 0.145 0.838 0.908 Note: Standard errors are in parenthesis




4.4 The Balance of Payments Constrained Growth

The estimates for the income and price elasticities of demand from the import and export

demand functions are applied to calculate the balance of payments constrained growth rates

given in Equations 3.4 to 3.7 and 2.9 to 2.10. These can be seen in Table 7 and include the

original weak version of Thirlwall’s law, yB, the strong version of Thirlwall’s law, *yB, the

balance of payments constrained growth rate with sustainable debt accumulation, yBSDA, the

balance of payments constrained growth with sustainable debt accumulation and interest rate

payments abroad, yBSDAR, and finally the two versions of the balance of payments constrained

growth with sustainable debt accumulation, interest rate payments and the terms of trade. In

the former version the terms of trade are interacted with the price elasticities of demand for

exports and imports, *yBSDART, and in the latter the terms of trade are only interacted with the

price elasticity of demand for imports, yBSDART.

The different balance of payments constrained growth rates are estimated for the entire sample

period which ranges from around the 1960s to 2014 period. This can be seen in Table 7 where

the estimated balance of payments constrained growth rates are compared with the actual

growth rate for the period concerned. We also estimate the balance of payments constrained

27

growth rate for the sub-periods 1960 to 1980 and 1980 to 2014 which can be seen in Appendix

G.

The balance of payments constrained growth model does a very good job at predicting the

actual growth rate for the region. The absolute difference between the actual growth rate and

the balance of payments constrained growth rate was less than 0.5 for 17 out of 22 countries

and less than one for 19 countries. The simple model best explained the growth process for

South Africa, Mali, Uganda and Zimbabwe as the absolute difference between the balance of

payments constrained growth rate and the actual growth rate was 0.18, 0.04, 0.84 and 0.06

respectively. The strong version of the model best explained the growth process for Kenya

where the difference was 0.42 while the model which allows for sustainable debt accumulation

best predicted the growth rate for Cameroon with an absolute error of 0.11.

The model with the most predictive power was the balance of payments constrained growth

with sustainable debt accumulation and interest payments abroad. The model closely predicted

the growth rates of the Democratic Republic of Congo, Sudan, Mauritius, Senegal, Sierra

Leone and Togo with an absolute error of 0.02, 0.15, 0.04, 0.17, 0.01 and 0.17 respectively.

This was closely followed by the balance of payments constrained growth which includes the

terms of trade interacted with the price elasticities of demand for imports and exports, which

closely predicted the growth rates of Nigeria, Botswana, Republic of Congo, Gabon,

Mozambique and Zambia with an error of 0.13, 0.98, 0.37, 0.04, 0.02 and 0.58 respectively.

Finally the balance of payments constrained growth rate which included the terms of trade and

only the price elasticity of demand for imports best predicted the growth rate of Gambia with

a difference of 0.27.

The model failed to make a reasonable prediction for the actual growth rate for three countries.

These are Namibia, Benin and Chad where the absolute difference between the actual and

predicted growth rate was 1.59, 2.11 and 10.91 respectively.

28

Table 7; The balance of payments constrained growth rate estimated for the 1960-2014 period

StartN AverageN

Period Country Actual 𝑦𝐵 ∗ 𝑦𝐵 𝑦𝐵𝑆𝐷𝐴 𝑦𝐵𝑆𝐷𝐴𝑅 ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 𝑦𝐵𝑆𝐷𝐴 𝑦𝐵𝑆𝐷𝐴𝑅 ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 𝑦𝐵𝑆𝐷𝐴𝑅𝑇

1975-2014 Benin 3.680 7.197 8.281 6.453 5.830 7.0800 6.066 5.880 5.788 6.981 6.090

1975-2014 Botswana 7.535 9.284 6.552 9.101 9.095 6.158 9.166 9.654 9.657 6.555 9.780

1960-2014 Cameroon 3.647 3.530 3.535 3.371 -0.461 3.314 3.514 3.405 -0.184 3.405

1960-2005 Chad 3.617 14.524 80.780 85.006 -27.788 58.628 67.030 67.866 -20.615 47.611

1960-2014 Congo, Dem.

Rep.

1.348 3.030 4.597 3.472 1.438 3.255 1.357 4.523 4.035 6.356 3.983

1960-2014 Congo Dem.

Rep.21 (OLS)

1.348 2.783 5.927 3.222 1.329 5.085 1.254 4.302 3.834 8.709 3.785

1960-2014 Congo, Rep. 4.501 5.082 2.428 5.953 5.326 2.128 4.867 3.418 3.001 0.287 1.831

1960-2014 Gabon 4.47 4.087 4.607 4.162 4.116 4.624 4.460 4.416

1960-2014 Gabon (OLS)22 4.47 5.322 6.436 5.263 4.776 5.572 4.430 5.261 5.083 5.871 4.755

1966-2013 Gambia 3.977 8.770 8.330 66.656 107.126 -127.012 -44.516 -13.443 -13.358 10.352 3.707

1960-2014 Kenya 4.789 4.161 4.369 4.167 3.969 3.906 3.621 4.180 4.137 4.034 3.807

1967-2007 Mali 3.731 3.683 2.953 2.271 2.099 1.674 2.152 1.699 1.639 1.343 1.697

1976-2014 Mauritius 4.581 4.872 3.975 4.809 4.617 3.924 4.831 4.558 4.512 3.934 4.778

1980-2014 Mozambique 5.044 4.907 7.399 3.035 2.644 5.021 3.452 1.668 1.625 3.444 2.595

1980-2014 Namibia 3.531 1.626 1.937 1.558 1.551 1.254 1.676 1.687 1.370

1980-2013 Nigeria 4.279 5.566 5.211 5.378 3.489 4.409 4.786 5.747 4.626 8.760 9.149

1960-2014 Senegal 2.829 3.107 1.936 2.996 2.543 0.446 1.630 3.027 2.975 1.014 2.161

1967-2014 Sierra Leone 3.137 3.811 3.150 2.240 2.650 3.382 3.242 3.624

1960-2014 South Africa 3.239 3.058 6.068 3.035 2.851 6.002 2.914 3.014 2.888 5.974 2.939

1960-2014 Sudan 3.934 5.900 2.658 5.901 3.813 -31.232 9.220 5.874 3.346 -32.290 8.212

1960-2014 Sudan (OLS) 3.934 5.864 5.864 3.789 9.161 5.841 3.324 8.164

1960-2014 Togo 3.934 5.243 4.201 3.761 3.692 3.279 3.142 3.058

1982-2014 Uganda 6.089 6.960 6.717 4.826 4.912 1.067 1.240 4.055 4.191 -0.251 -0.099

1982-2014 Uganda (OLS) 6.089 5.245 3.199 3.222 1.356 2.576 2.599 0.536

1960-2013 Zambia 3.389 2.007 6.271 1.607 -0.634 3.965 0.05 1.369 0.865 4.507 1.506

1976-2014 Zimbabwe 1.586 1.528 37.24 1.469 0.319 35.494 1.390 1.502 1.476 35.947 2.396

21 For the Democratic Republic of Congo both the import and export demand function use OLS. 22 For Gabon both the import and export demand function use OLS.

29

Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio. Average refers to the average value for these two

ratios for the period considered

𝑦𝐵,is the ‘weak’ original version of the balance of payments constrained growth model

𝑦𝐵,is the ‘strong’ original version of the balance of payments constrained growth model



∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments abroad and the terms of trade interacted with the price elasticities of demand

for imports and exports

𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments and the terms of trade (only the income and price elasticities from the import


OLS indicates the growth rates that have been estimated using the import and export demand functions derived from OLS

30

4.5 Formally Testing the Balance of Payments Constrained Growth Model

We were able to estimate the balance of payments constrained growth rate for 22 countries.

We begin by formally testing the model for each individual country. A summary of the results

can be seen in Table 8. For 18 countries, which is almost 82% of the countries included in the

analysis, we could not reject the null hypothesis for the equality between the estimated income

elasticity of demand for imports and the hypothetical income elasticity of demand for imports

that would exactly equate the actual growth rate of the country concerned for at least one of

the balance of payments constrained growth models using the Wald test. This provides strong

evidence that these 18 African countries were indeed balance of payments constrained during

the 1960 to 2014 period. These results are consistent with Hussain (1999) who found evidence

in favour of the model for 26 out of 29 African countries23.

The balance of payments constrained growth with sustainable debt accumulation and interest

rate payments abroad best explained the growth process of the region as we found evidence of

the equality of the estimated income elasticity of demand and the hypothetical income elasticity

of demand for 17 of the 18 countries. This highlights the important role of capital flows to the

region as well as the significance of interest rate payments abroad. The results are similar to

those obtained by Moreno-Brid (2003) for Mexico.

This was followed closely by the original version of the model which was able to explain the

growth experience of 16 countries. This is not surprising as a study by Hussain (1999) found

that the basic and extended model which allows for capital flows, were good predictors for the

actual growth rate in Africa and Asia. Perraton (2003) for a group of developing countries,

additionally found that the original version of the model slightly outperformed the extended

model with the terms of trade as it held for the majority of the countries included in the analysis.

23 Hussain (1999) study included North Africa, which is excluded here.

31

Using the individual country test, we could not find evidence for any of the balance of payments

constrained growth models for Benin, Botswana, Chad and Namibia. This result is not

surprising for Benin and Chad as the estimated balance of payments constrained growth rate

given in Table 7 had little predictive power for the actual growth rate. For Namibia this may

be due to the lack of data on interest payments abroad.

Caution is needed when rejecting the balance of payments constrained growth model for

Botswana based on the Wald test as the estimated income elasticity is 0.896 while the

hypothetical income elasticity for the model with sustainable debt accumulation, interest

payments abroad and the terms of trade is 0.81; a difference of 0.08. No other studies have

been done for Botswana, Chad and Namibia; however a study by Perraton (2003) included

Benin, found evidence in favour of the original and extended model which includes the terms

of trade effects.

There is very little difference in the results from the Wald test when testing the balance of

payments constrained growth rate estimated using the average ratios and the start of period

ratios for the share of exports in imports and the share of interest payments abroad in imports.

For the latter, the result is in line with the literature as we expect the share of interest payments

abroad to have a limited effect on the balance of payments constrained growth rate (Thirlwall,

2012).

As the balance of payments constrained model is a long run growth model, the results from the

two sub-periods are reported in Appendix H. It is interesting to note that during the overall

period and the 1980 to 2014 period, the balance of payments constrained growth model with

sustainable debt accumulation and interest rate payments abroad best explained the growth

process of the region. However the same model performed relatively worse during the 1960 to

1980 period as it had the least predictive power. This highlights the growing role of capital

flows and interest payments abroad in the region.

32

Table 8; Wald test results for the equality of the estimated income elasticity of demand, �̂�, and the hpothetical income elsasticity of demand, 𝜋𝐻 , 1960 − 2014

Average Start

Period Country �̂� 𝜋𝐻𝐵 ∗ 𝜋𝐻𝐵 𝜋𝐻𝐵𝑆𝐷𝐴 𝜋𝐻𝐵𝑆𝐷𝐴𝑅 ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴 𝜋𝐻𝐵𝑆𝐷𝐴𝑅 ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇

1960-

2013

Benin 1.142 2.233 2.569 1.640 1.512 1.727 1.553 1.440 1.426 1.586 1.466

F statistic 118.00*** 170.28*** 20.71*** 11.42*** 28.58*** 14.10*** 7.40** 6.72** 16.46*** 7.70***

P Value 0.000 0.000 0.000 0.002 0.000 0.000 0.010 0.014 0.000 0.009

1975-

2014

Botswana 0.896 1.104 0.779 1.125 1.121 0.697 1.131 1.078 1.073 0.813 1.084

F statistic 77.66*** 24.59*** 94.14*** 90.88*** 71.13*** 99.13*** 59.46*** 56.23*** 12.38*** 63.44***

P Value 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000

1960-

2014

Cameroon 1.379 1.335 1.336 1.281 1.260 1.329 1.311 1.290

F statistic 0.25 1.26 1.86 0.33 0.61 1.04

P Value 0.621 0.268 0.180 0.567 0.438 0.313

1960-

2005

Chad 0.656 2.634 1.637 1.623 0.282 1.309 1.655 1.650 0.280 1.337

F statistic 104.46*** 38.90*** 37.79*** 5.69** 17.22*** 40.34*** 39.93*** 5.75** 18.73***

P value 0.000 0.000 0.000 0.024 0.000 0.000 0.000 0.024 0.000

1960-

2014

Congo, Dem.

Rep. 2.179 4.898 7.431 6.099 2.336 5.508 2.195 10.999 9.539 15.896 9.397

F statistic 4.61** 17.19*** 9.58*** 0.02 6.91** 0.00 48.49*** 33.77*** 117.28*** 32.48***

P value 0.038 0.000 0.003 0.902 0.012 0.990 0.000 0.000 0.000 0.000

1960-

2014

Congo, Dem.

Rep. (OLS) 2.372 4.898 10.431 6.099 2.336 9.431 2.195 10.999 9.539 23.588 9.397

F statistic 17.41*** 177.25*** 37.90*** 0.00 135.99*** 0.09 203.12*** 140.18*** 1228.56*** 134.68***

P value 0.000 0.000 0.000 0.952 0.000 0.770 0.000 0.000 0.000 0.000

1960-

2012

Congo, Rep. 1.483 1.674 0.800 2.224 1.886 0.321 1.662 1.270 1.195 0.675 0.971

F statistic 0.43 5.49** 6.73** 1.91 15.89*** 0.38 0.54 0.98 7.69** 3.09*

P value 0.522 0.032 0.019 0.186 0.001 0.548 0.474 0.337 0.013 0.098

1960-

2014

Gabon 1.275 1.165 1.348 1.116 1.093 1.359 1.269 1.246

F statistic 0.51 0.22 1.06 1.39 0.29 0.00 0.04

P value 0.479 0.643 0.308 0.245 0.594 0.965 0.848

33

24 For Gabon both the import and export demand functions are estimated with OLS. 25 For Mali the ARDL estimates for the import and export demand function are used. 26 For Namibia there is no data on interest payments abroad.

1960-

2014

Gabon24

(OLS) 0.979 1.165 1.409 1.348 1.116 1.473 0.961 1.359 1.269 1.642 1.114

F statistic 0.43 2.28 1.68 0.23 3.01* 0.00 1.78 1.04 5.43** 0.22

P value 0.517 0.137 0.201 0.633 0.089 0.948 0.188 0.313 0.024 0.638

1966-

2013

Gambia 0.475 1.048 0.994 1.027 0.838 0.014 0.304 1.019 1.017 0.276 0.483

F statistic 8.74*** 7.17** 8.11*** 3.51* 5.66** 0.78 7.88*** 7.82*** 1.05 0.00

P value 0.005 0.011 0.007 0.069 0.022 0.383 0.008 0.008 0.311 0.967

1960-

2014

Kenya 0.986 0.857 0.900 0.871 0.875 0.867 0.828 0.892 0.893 0.878 0.846

F statistic 0.37 0.16 0.29 0.27 0.31 0.55 0.20 0.19 0.26 0.43

P value 0.547 0.687 0.591 0.604 0.578 0.461 0.660 0.663 0.613 0.513

1967-

2007

Mali25 2.195 2.166 1.737 1.544 1.478 1.291 1.501 1.371 1.350 1.231 1.374

F statistic 0.00 0.18 0.37 0.45 0.71 0.42 0.59 0.62 0.18 0.59

P value 0.978 0.671 0.547 0.508 0.405 0.521 0.447 0.436 0.374 0.449

1976-

2014

Mauritius 1.183 1.258 1.026 1.238 1.191 1.028 1.241 1.178 1.170 1.060 1.220

F statistic 0.20 0.90 0.11 0.00 0.88 0.12 0.00 0.01 0.56 0.05

P value 0.653 0.354 0.744 0.962 0.360 0.730 0.975 0.937 0.465 0.826

1980-

2014

Mozambique 1.877 1.826 2.753 1.356 1.265 1.871 1.471 1.160 1.152 1.538 1.358

F statistic 0.01 3.75* 1.33 1.84 0.00 0.81 2.52 2.57 0.56 1.32

P value 0.910 0.066 0.261 0.189 0.989 0.378 0.127 0.123 0.461 0.263

1980-

2014

Namibia26 1.946 0.896 1.067 0.904 0.901 0.743 0.892 0.909 0.731

F statistic 32.35*** 22.68*** 31.86*** 32.05*** 42.46*** 32.60*** 31.56*** 43.31***

P value 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1985-

2013

Nigeria 0.941 1.224 1.146 1.504 0.572 1.001 1.177 1.149 0.987 1.504 1.592

F statistic 0.89 0.47 3.53* 1.52 0.04 0.62 0.48 0.02 3.53* 4.72**

P Value 0.359 0.504 0.078 0.235 0.845 0.443 0.498 0.881 0.078 0.045

1960-

2014

Senegal 1.107 1.215 0.757 1.156 1.027 0.440 0.771 1.169 1.153 0.538 0.897

F statistic 1.75 18.64*** 0.36 0.98 67.61*** 17.18*** 0.57 0.31 49.21*** 7.72**

P value 0.193 0.000 0.553 0.328 0.000 0.000 0.453 0.578 0.000 0.013

34

27 Sierra Leone uses the ARDL model. 28 Sudan uses the ARDL estimate for both the export and import demand function. 29 For Uganda both import and export demand functions are estimated with the ARDL model.

1967-

2014

Sierra Leone27 2.310 2.806 2.318 1.747 2.004 2.476 2.380 2.638

F statistic 0.26 0.00 0.33 0.10 0.03 0.01 0.11

P value 0.615 0.994 0.567 0.755 0.866 0.944 0.739

1960-

2014

South Africa 0.955 0.901 1.789 0.882 0.821 1.905 0.843 0.857 0.805 2.119 0.827

F statistic 0.01 2.31 0.02 0.06 2.99* 0.04 0.03 0.07 4.50** 0.02

P Value 0.922 0.136 0.894 0.808 0.09 0.839 0.859 0.785 0.039 0.880

1964-

2013

Sudan28 0.957 1.435 0.646 1.435 0.978 -7.365 2.208 1.484 0.802 -8.564 2.081

F statistic 5.87** 2.50 5.87** 0.01 1784*** 40.26*** 7.14*** 0.62 2333*** 32.50***

P Value 0.019 0.121 0.019 0.917 0.000 0.000 0.010 0.434 0.000 0.000

1964-

2013

Sudan (OLS) 0.963 1.435 1.435 0.978 2.208 1.484 0.802 2.081

F statistic 0.76 0.70 0.00 4.89** 0.86 0.08 3.95*

P Value 0.388 0.406 0.980 0.031 0.359 0.774 0.052

1960-

2014

Togo (OLS) 1.608 2.143 1.690 1.555 1.534 1.442 1.408 1.387

F statistic 1.16 0.03 0.01 0.02 0.11 0.16 0.17

P value 0.286 0.870 0.914 0.888 0.738 0.687 0.678

1982-

2014

Uganda29 1.553 1.775 1.713 1.345 1.365 0.753 0.781 1.257 1.294 0.689 0.710

F statistic 0.87 0.45 0.78 0.64 11.43*** 10.64*** 1.57 1.20 13.33*** 12.69***

P value 0.369 0.514 0.395 0.440 0.005 0.006 0.233 0.294 0.003 0.003

1982-

2014

Uganda

(OLS)

2.061 1.775 1.345 1.365 0.912 1.257 1.294 0.841

F statistic 0.22 1.37 1.29 3.52* 1.72 1.57 3.96*

P value 0.644 0.252 0.265 0.071 0.200 0.221 0.056

1960-

2014

Zambia 4.562 2.702 8.441 2.290 0.085 5.203 0.853 2.065 1.540 5.901 2.308

F statistic 0.74 3.20* 1.10 4.26* 0.09 2.92 1.32 1.94 0.38 1.08

P value 0.406 0.097 0.314 0.059 0.772 0.111 0.270 0.187 0.547 0.317

1976-

2014

Zimbabwe 1.167 1.124 27.399 1.097 0.440 20.622 1.054 1.111 1.093 24.110 1.708

F statistic 0.03 12190*** 0.09 9.37*** 6705*** 0.23 0.06 0.10 9324*** 5.18**

P value 0.857 0.000 0.770 0.005 0.000 0.638 0.815 0.758 0.000 0.032 Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio. Average refers to the average value for these two ratios

for the period considered

35

𝜋𝐻𝐵, is the hypothetical income elasticity of demand from the original “weak” version of the balance of payments constrained growth model

∗ πHB, is the hypothetical income elasticity of demand from the original “strong” version of the balance of payments constrained growth model

𝜋𝐻𝐵𝑆𝐷𝐴, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation

𝜋𝐻𝐵𝑆𝐷𝐴𝑅, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation and interest payments abroad

∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation, interest payments abroad and the

terms of trade interacted with the price elasticities of demand for imports and exports.

𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation, interest payments and the terms of

trade (only the income and price elasticities from the import demand function are included)




36

Our second formal test for the balance of payments constrained model can be seen in Table 9.

We regressed each of our calculated balance of payments constrained growth rates on the actual

growth rate for all 22 countries. We use two different specifications; with and without a trend.

When we exclude the trend, we find strong evidence in support of the balance of payments

constrained model as the coefficient on the actual rate of growth ranged from 0.846 to 1.14. In

addition, using the Wald test, we accept the hypothesis that the coefficient is equal to one.

These results confirm and strengthen the results obtained from the single country tests. As

Benin, Botswana, Chad and Namibia were included in the regressions below, it would be

erroneous to dismiss the balance of payments constrained growth as being irrelevant for these

countries. The results below use the logarithmic form, please see Appendix I for the results

from the alternative level specification.

Table 9; Regression results of the balance of payments constrained growth, 𝑦𝐵 , on the actual growth rate

(logarithmic form)

Dependent

variable

Constant,

α

Coefficient

on the

actual

growth

rate, β R2 F statistic

Wald test

(β=1)

P value

Wald test

(α=0)

P value

𝑦𝐵 0.382 0.834*** 0.325 9.65*** 0.544 0.308

(0.366) (0.268)

𝑦𝐵 1.104*** 0.918 234.95*** 0.161

(0.072)

∗ 𝑦𝐵 2.371*** -0.539 0.102 1.59 0.002*** 0.001***

(0.578) (0.427)

∗ 𝑦𝐵 1.132*** 0.715 37.75*** 0.482

(0.184)

AverageN 𝑦𝐵𝑆𝐷𝐴 0.617 0.712 0.070 1.51 0.625 0.443

(0.791) (0.579

𝑦𝐵𝑆𝐷𝐴 1.148*** 0.726 55.86*** 0.344

(0.153)

𝑦𝐵𝑆𝐷𝐴𝑅 -0.396 1.403** 0.192 4.28** 0.559 0.676

(0.932) (0.678)

𝑦𝐵𝑆𝐷𝐴𝑅 1.126*** 0.663 37.36*** 0.499

(0.184)

∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 1.960** -0.457 0.044 0.60 0.028** 0.029**

(0.798) (0.591)

37

∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 0.921*** 0.570 18.56*** 0.720

(0.213)

𝑦𝐵𝑆𝐷𝐴𝑅𝑇 -0.230 1.008 0.091 1.90 0.990 0.819

(0.997) (0.731)

𝑦𝐵𝑆𝐷𝐴𝑅𝑇 0.846*** 0.483 18.71*** 0.441

(0.195)

StartN 𝑦𝐵𝑆𝐷𝐴 0.793 0.417 0.036 0.72 0.251 0.252

(0.671) (0.492)

𝑦𝐵𝑆𝐷𝐴 0.977*** 0.719 51.36*** 0.869

(0.136)

𝑦𝐵𝑆𝐷𝐴𝑅 0.433 0.723 0.038 0.71 0.284 0.316

(0.513) (0.701)

𝑦𝐵𝑆𝐷𝐴𝑅 0.941*** 0.692 42.86 0.685

(0.143)

∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 2.522** -0.854 0.103 1.62 0.015** 0.014**

(0.906) (0.670)

∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇 0.924*** 0.491 14.50*** 0.759

(0.242)

𝑦𝐵𝑆𝐷𝐴𝑅𝑇 1.113 0.118 0.002 0.05 0.112 0.140

(0.724) (0.531)

𝑦𝐵𝑆𝐷𝐴𝑅𝑇 0.904*** 0.644 38.0*** 0.522

(0.146) Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in

imports ratio. Average refers to the average value for these two ratios for the period considered.



∗ 𝑦𝐵,is the ‘strong’ original version of the balance of payments constrained growth model



∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments abroad

and the terms of trade interacted with the price elasticities of demand for imports and exports.

𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments and the

terms of trade (only the income and price elasticities from the import demand function are included)




38

5. Concluding Remarks

The balance of payments constrained growth rate was estimated for 22 sub-Saharan African

countries. The model proved to have strong predictive power as it was able to closely predict

the growth rate of 17 countries with an absolute error of less than 0.5. This figure increased to

19 at an absolute error below one.

When formally testing the model for each individual country, by testing the equality between

the estimated income elasticity of demand for imports and the hypothetical income elasticity

of demand for imports that would exactly equate the actual rate of growth, again we find strong

evidence in support of the balance of payments constrained growth model. For 18 countries we

found evidence in support of at least one of the balance of payments constrained growth

models.

The model which accounts for sustainable debt accumulation and interest rate payments abroad

outperformed all the other models both in its predictive power and when testing the equality of

the estimated and hypothetical income elasticities of demand. It was able to explain the growth

experience of 77.3% of the countries included in the study. This highlights the importance of

capital flows and interest rate payments in the region.

Unsurprisingly, the same countries where the balance of payments constrained growth model

had poor predictive power, failed the formal test. These are Benin, Botswana, Chad and

Namibia. Caution however is needed when rejecting the balance of payments constrained

growth rate for Namibia as data on interest payments abroad was not available. By applying

only the simple balance of payments constrained growth model, we could erroneously reject

the model when it actually does apply. This would have been the case for the Democratic

Republic of Congo and Gambia. It is therefore important to account for capital flows and

interest payments abroad.

39

When pooling the results from the 22 countries, we find strong evidence in favour of all 6

models for the balance of payments constrained growth for the full sample of countries,

including Benin, Botswana, Chad and Namibia. These results strengthen those obtained from

the single country tests.

Our results provide strong evidence that the demand-led long run growth model developed by

Thirlwall (1979), is relevant for the sub-Saharan African region. One of the implications of the

balance of payments constrained growth model is that the structure of production and exports

determines the income elasticity of demand for exports which therefore determines the rate of

growth of one country relative to another. What a country exports has to do with how its

economic activity is structured. Changing the structure of the economy is therefore imperative

in order to bring about long term economic growth and development in the region.

40

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45

Appendix A

The starting point for the extended model of the balance of payments constrained growth rate

is the balance of payments accounting identity in disequilibrium (Hussain and Thirlwall, 1982)

𝑃𝑑𝑋 + 𝐶 = 𝑃𝑓𝑀𝐸 (Equation 1)

where, C, is the nominal value of net capital inflows measured in the domestic currency30. If

C<0, there are net capital outflows and if C>0, there are net capital inflows. The rest of the

variables are defined as before.

The first two terms in Equation 1 represent the items that provide foreign currency inflows

while the right hand side of the equation represents the imports that have to be paid for in

foreign currency. Taking the first difference of the variables in logarithmic form yields,

𝜃(𝑝𝑑 + 𝑥) + (1 − 𝜃)(𝑐) = 𝑝𝑓 + 𝑚 + 𝑒 (Equation 2)

where, 𝜃, and (1-𝜃), represent the share of exports and capital flows as a proportion of total

receipts respectively. Therefore, 𝜃 = 𝑃𝑑𝑋/𝑅 and (1 − 𝜃) = 𝐶/𝑅, where R is total receipts

which can also be expressed as the import bill financed by export earnings and capital flows.

x, is the growth rate of exports, c, is the growth rate of capital flows, m, is the growth rate of

imports, pd, is the growth rate of domestic prices and pf, is the growth rate of import prices.

The import and export demand functions given in Equations 2.5 and 2.6 are substituted into

Equation 2 then solved for the growth of balance of payments constrained income,

∗∗∗ 𝑦𝐵 = [(1 + 𝜃𝜂 + 𝜓)(𝑝𝑑 − 𝑝𝑓 − 𝑒) + 𝜃휀𝑧 + (1 − 𝜃)(𝑐 − 𝑝𝑑))]/𝜋 (Equation 3)

It can be seen from Equation 3 that any country’s growth rate in principle can be

disaggregated into four component parts (Thirlwall, 2011):

1. The growth associated with real terms of trade movements: (pd – pf –e)/π

30 For simplicity the nominal exchange rate is assumed to be fixed and equal to one (Moreno-Brid, 2003).

46

2. Growth associated with terms of trade movements combined with price elasticities of

exports and imports: ((1 + 𝜃𝜂 + 𝜓) (pd – pf –e))/π

3. Growth related to exogenous changes in income growth abroad: 𝜃휀𝑧/π

4. Growth effects of real capital flows31: (1-𝜃)(𝑐 − 𝑝d)]/π

Note that if relative prices measured in a common currency remain unchanged, that is 𝑝𝑑 =

𝑝𝑓 + 𝑒, the current account is balanced and there are no capital flows, then the balance of

payments constrained income growth in Equation 3 will be reduced to its basic form expressed

in Equation 2.10 in section 2.

31Growth in Real capital inflows are defined as (c-pd).

47

Appendix B

Data and sources for calculating the balance of payments constrained growth rate

Variable Source

Exports of goods and services (constant 2005 USD) World Development Indicators (World Bank)

Imports of goods and services (constant 2005 USD) World Development Indicators (World Bank)

GDP (constant 2005 USD) World Development Indicators (World Bank)

GDP deflator (base year 2005) World Development Indicators (World Bank)

Consumer price index (CPI) World Development Indicators (World Bank)

World Income, less own country income (constant

2005 USD)

World Development Indicators (World Bank)

Export price index (unit value of exports, f.o.b)

(Base year 2005)

International Financial Statistics (IMF)

Import price index (unit value of imports, f.o.b)

(Base year 2005)

International Financial Statistics (IMF)

Interest payment on external debt (constant 2005

USD)

World Development Indicators (World Bank)

REER (Real effective exchange rate, CPI-based) REER database (Bruegel)

REER measures the development of the real value of a country’s currency against the basket

of the trading partners of the country. It therefore can be expressed as Pd/Pf or Pd/Pm which is

domestic to foreign prices.

We use REER to estimate the import and export demand functions. In the export demand

function, we make use of the domestic to foreign price ratio, Pd/Pm. REER is therefore used

in the export demand function. For the import demand function, we make use of the foreign to

domestic price ratio, Pf/Pd, 1/REER is therefore used in the import demand function.

Other price indices were also used when REER was not available. We use the price index

recommended by Tharnpanich and McCombie (2013).

𝑅𝑃𝑀2 =𝐼𝑚𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥

𝐺𝐷𝑃 𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟


𝐶𝑃𝐼


𝐸𝑥𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥

𝑅𝑃𝑋4 =𝐸𝑥𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥

𝑖𝑚𝑝𝑜𝑟𝑡 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥

48

Appendix C

The results from the unit root tests are shown below. Included are the Clemente, Montanes and Reyes (CMR) unit root test where,

Sudden changes in the series are captured by the Additive Outliers (AO)

Gradual shift in the mean of the series is detected by the Innovational Outliers (IO)

Results from the unit root tests

Country Variable

CMR2

(AO) Breaks

CMR1

(AO) Break CMR2 (IO) Breaks CMR1 (IO) Break ADFN

ADF

NC

ADF

trend PP PP NC PP trend

Kenya In_X -3.742 1987***

2004***

-4.032 1984***

2001***

-0.543 3.542 -2.222 -0.767 3.882 -2.755

∆In_X -7.503*** 1988 1995

-1.107 1988 -9.532*** 1971 1989

-9.105*** 1989 -6.169*** -8.607***

In_M -3.555 1994***

2007***

-3.449 1991***

2001***

0.674 2.532 -1.076 0.763 2.179 -1.141

∆In_M -3.901 1978**

1981**

-5.064 1980

1982*

-4.532** 1982** -4.745*** -7.012***

In_Y 2.265 1974*** 1991***

-4.802 1969** 2002***

-2.360 5.344 -2.409 -1.362 7.060 -1.491

∆In_Y -4.532 1968

1973**

-8.264*** 1980** -10.853*** 1969***

1973***

-5.077*** -7.222***

In_ZY -3.412 1980***

2000***

-4.406 1982**

1995***

-3.367** -4.716***

In_REER -2.234 1987*** 1998***

-3.526 1986*** 1992***

-1.314 0.134 -0.739 -1.478 0.144 -0.921

∆In_REER -3.361 1986*

1991***

-6.926*** 1986***

1992***

-4.991*** -7.660***

In_RPM3 -1.373 1995*** -0.348 1982**

1989***

0.658

(2lag)

-1.112 -0.897 1.028 -1.278 -0.639

∆In_RPM3 -1.960 1982*** -2.566 1979*** -2.475 -2.117 -3.139* -3.655*** -3.329*** -4.265*** In_RPM4 -4.128 1975***

1984***

-4.515 1969**

1976**

-1.157 -1.835 -2.230 -1.044 -1.698 -2.701

∆In_RPM4 -5.591*** 1975 -8.910*** 1976 -4.626*** -7.389***

Nigeria In_X -5.335 1986**

2003***

-4.980 1995***

2004***

-0.934 1.015 -2.646 -1.193 0.822 -3.312*

∆In_X -0.863 2010 -4.131* 2001 -4.547*** -6.907*** In_M -3.790 1997*

2004***

-3.764 1999*** -1.040 0.232 -3.507** -4.934***

In_Y -3.101 1997*** 2005***

-3.891 1986*** 2002***

1.081 2.198 -1.914 1.152 2.642 -1.775

∆In_Y -5.563*** 2002*** -6.362*** 2003 -3.431*** -4.158***

49

In_ZY -2.597 1991***

2001***

-2.240 2009 -1.551 4.353 -2.759 -0.956 11.493 -1.192

∆In_ZY -2.898 2007** -5.469** 2006** -4.299*** -4.734***

In_REER -5.563*** 1988*** -4.201* 1984*** -2.891** -2.144* -0.700 -2.043

∆In_REER -4.368*** 1985 -5.225*** 1986 -3.329** -4.133***

Sudan In_X -4.024 1986**

2000***

-4.809 1983**

1996***

-0.497 1.102 -1.261 -0.371 1.265 -1.144

∆In_X -6.873*** 1997** -8.009*** 1996*** 1998**

-8.470*** -5.475***

In_M -3.485 1976***

2001***

-3.560 1994*** -1.180 0.755 -2.002 -1.462 0.855 -2.231

∆In_M -3.778** 2010* -8.419*** 1994**

2003**

-4.890*** -7.697***

In_Y32 -2.829 1978*** 1999***

-2.045 1972** 1994***

0.743 3.138 -2.530 0.797 4.599 -2.131

∆In_Y -2.873 1988 -3.397 1989 -5.229*** -5.099***

In_ZY -3.412 1980*** 2000***

-4.404 1982** 2005***

-3.367** -4.719***

In_REER 0.921 1989*** 1.986 1990*** 2004***

-2.200 0.158 -2.098 -2.908** 0.283 -2.884

∆In_REER 0.572 1990 -16.03*** 1990***

1994***

-5.831*** -9.464***

South Africa In_X -2.680 1989***

1997***

-4.160 1983*

1991***

-0.337 2.867 -1.779 -0.503 3.819 -1.713

∆In_X -6.293*** 1993 -6.567*** 1990* 2007**

-5.198*** -6.034***

In_M -1.136 1992*** 2004***

-3.243 1992*** 2002**

-0.879 2.295 -2.243 -0.379 2.786 -1.879

∆In_M -5.137* 1975**

1985**

-7.207*** 1970**

1984*

-6.040*** -6.488***

In_Y33 -3.162 1975***

2001***

-6.091*** 1992***

2002**

-1.999 2.719 -3.240* -2.625* 6.278 -2.925

∆In_Y -4.932* 1983*** 1994**

-5.288*** 1970*** -3.035** -4.076***

In_ZY -3.409 1980***

2000***

-4.394 1982**

1995***

-3.564*** -4.716***

In_REER -5.491** 1981***

1997***

-4.270 1982***

1996***

-1.442 -1.036 -

4.388***

-1.157 -1.242 -3.518**

∆In_REER -4.673*** 2000 -6.030*** 2001* -6.379*** -6.285

32 For Sudan In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 33 For South Africa In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

50

Benin In_X -3.017 1970***

1993***

-3.397 1988*** -1.617 2.023 -3.576** -0.960 2.466 -2.432

∆In_X -7.207*** 1996 -7.315*** 1970** -6.345***

-5.319***

In_M -4.063 1972*** 1994***

-3.996 1988*** -2.143 2.158 -3.368* -1.353 2.429 -2.212

∆In_M -3.576 1979**

1987*

-5.691*** 1980***

1988***

-4.244*** -5.760***

In_Y34 -1.649 1982***

1998***

-1.143 1977***

1994**

1.316 5.456 -1.967 1.708 10.022 -1.747

∆In_Y -3.391* 1098 -3.747 1988*** -6.199*** -7.054***

In_ZY -3.412 1980***

2000***

-4.403 1982**

1995***

-3.367** -4.715***

In_REER -2.768 1976*** 1984***

-6.015***

1973*** 1979***

-2.436 -1.505 -1.408 -2.465 -1.700 -1.195

∆In_REER -4.673*** 1992 -6.914*** 1982** -4.530*** -6.090***

Botswana In_X -3.886 1984*** 1996***

-3.043 1980 -2.068 2.457 -2.423 -2.688* 3.082 -2.709

∆In_X -3.102 2007 -6.067*** 1987*** -4.695*** -6.052***

In_M -3.003 1990*** 2009***

-3.233 1985** 2005**

-0.960 2.351 -3.585** -0.992 3.724 -2.838

∆In_M -3.673** 1995 -6.038*** 1989**

1996*

-4.952*** -4.750***

In_Y -3.063 1985***

1999***

-2.149 2012 -3.408** 3.059 -2.175 -4.562***

∆In_Y -7.141*** 1986*** 1990***

-3.966 1990*** -3.988*** -4.002***

In_ZY -2.901 1989*** 2001***

-1.904 1981 -0.951 4.184 -2.175 -1.611 12.175 -2.692

∆In_ZY -3.814** 2007** -5.260*** 2006* -4.363*** -4.701***

In_REER -3.786 1986*** 1999***

-2.029 1983 -1.731 0.147 -1.703 -1.818 0.083 -1.742

∆In_REER -3.269 1982*

1988***

-4.811*** 1983 -7.092*** 1983***

1987***

-4.109*** -5.364***

Cameroon In_X -1.019 1975***

1981***

-4.472 1967**

1976***

-0.735 2.265 -1.685 -0.567 2.490 -1.784

∆In_X -3.888 1975*** 1985***

-7.047*** 1976*** 1984***

-5.408*** -6.973***

In_M35 -3.461 1978***

2001***

-2.190 1974**

1991*

0.233 3.153 -2.488 0.353 3.458 -2.808

34 For Benin In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 35 For Cameroon In_M, 4 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

51

∆In_M -8.078*** 1987**

1990**

-8.175*** 1985***

1991***

-6.203*** -7.989***

In_Y -3.229 1979***

2002***

-3.211 1975**

1999**

-0.898 1.355 -3.051 -0.658 3.431 -1.556

∆In_Y -2.394 1986*** 1991***

-7.521*** 1985*** 1992***

-3.174** -5.349***

In_ZY -3.415 1980***

2000***

-4.405 1982**

1995***

-3.365** -4.713***

∆In_ZY -4.469 1971***

2007**

-7.376*** 1972***

2006***

In_REER -1.525 1985** 1991***

-7.547*** 1973** 1992***

-1.568 -0.350 -2.221 -1.945 -0.471 -2.555

∆In_REER -12.344*** 1992 -5.668*** -8.171***

Chad In_X -0.576 1980*** 2002***

-6.354*** 1981*** 2002***

-1.046 1.064 -2.853 -0.972 1.244 -2.539

∆In_X -5.230** 2002** -7.036*** 1981 -6.038*** -7.026***

In_M36 -1.192 1986*** 1998***

-5.683** 1981*** 2000***

-2.403 0.626 -4.144***

-2.609* 0.385 -3.240*

∆In_M -3.671** 2000 -4.299** 1999 -4.400*** -5.955***

In_Y -0.472 1993*** 2006***

-3.655 1983*** 2001***

1.352 2.340 -1.017 1.601 2.603 -0.902

∆In_Y -5.556*** 2002** -7.188*** 1978* -4.311*** -5.945***

In_ZY -3.413 1980*** 2000***

-4.405 1982** 1995***

-3.368** 3.721 -2.958 -4.718*** 10.620 -2.691

∆In_ZY -4.470 1971***

2007**

-7.374*** 1972***

2006**

In_REER -3.125 1980***

1991***

-5.845** 1980***

1992***

-1.275 -1.015 -1.713 -1.219 -1.172 -1.642

∆In_REER -8.085*** 1992*

1996**

-9.213*** 1993* -5.160*** -6.182***

Congo, Dem. Rep.

In_X -4.374 1979*** 2004***

-3.167 1981* 2000***

-0.256 1.591 -1.768 -0.294 1.898 -1.771

∆In_X -8.014*** 1989**

1994***

-7.998*** 1990***

1993***

-5.626*** -6.699***

In_M -6.038*** 1976***

2004***

-2.155 1996** -1.096 1.224 -2.142 -1.174 1.513 -2.098

∆In_M -5.260* 1990*** 1993***

-5.506*** -6.147***

In_Y37 -3.793 1994***

2007***

-3.471 1988***

2005***

-2.122 0.470 -1.756 -1.078 0.764 -0.906

∆In_Y -5.070 1989***

1999***

-5.671** 1988***

2000***

-1.955 -1.900 -1.998 -3.007**

36 For Chad In_M, 3 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 37 For the Democratic Republic of Congo In_Y, 3 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

52

In_ZY -2.953 1980***

1999***

-4.180 1982**

1995***

-2.671* 3.959 -2.932 -4.221***

∆In_ZY -7.444*** 1971***

2007**

-7.228*** 1972***

2006**

In_REER -3.458* 1985*** -5.292* 1982*** 1999**

-1.563 -0.759 -2.495 -2.023 -1.105 -2.693

∆In_REER -3.141 1997 -7.918*** 1999**

2004**

-5.053*** -7.002***

Congo, Rep. In_X -3.563 1981***

1994***

-3.837 1978**

2007**

-1.298 2.064 -1.657 -2.281 3.640 -2.165

∆In_X -6.353*** 1981* -6.310*** 1982 -4.585*** -5.965***

In_M -4.273 1990***

2004***

-4.441 1991***

2004***

-0.174 1.639 -2.554 -0.212 1.827 -2.604

∆In_M -1.102 1980 -5.873*** 1992 -5.348*** -7.076*** In_Y38 -4.228 1983***

2007***

-4.643 1976***

2003***

-1.125 2.046 -2.485 -1.433 3.559 -2.092

∆In_Y -5.174* 1979*** 1982***

-4.514** 1981*** -3.552*** -3.781***

In_ZY -2.977 1985***

2000***

-3.023 1982*

1995**

-1.610 4.401 -3.243* -2.269 12.538 -2.697

∆In_ZY -5.894*** 1980** -5.898*** 1972* -4.962*** -4.915***

In_REER -1.721 1982***

1990***

-4.785 1979***

1986**

-1.444 -0.787 -1.364 -1.531 -1.112 -1.093

∆In_REER -6.521*** 1992 -7.062*** 1993* -4.841*** -5.388***

Gabon In_X -2.111 1971***

1990***

-8.203*** 1972***

1987***

-3.351** -3.663***

∆In_X -1.856 1977***

In_M -3.771 1971*** 1975***

-6.102*** 1972*** -2.758* -2.962**

∆In_M -2.053 1972

In_Y -1.139 1971*** 1991***

-3.872 1971*** 1986***

-1.900 1.867 -2.169 -2.323 2.495 -2.161

∆In_Y -2.691 1971*

1974***

-2.436 1973 -4.325*** -5.287***

In_ZY -3.412 1980***

2000***

-4.401 1982**

1995***

-3.363** -4.711***

∆In_ZY -4.474 1971*** 2007***

-7.372*** 1972*** 2006**

In_REER -5.376 1975***

1991***

-7.030*** 1973***

1992***

-0.718 -1.025 -1.793 -0.793 -0.939 -2.033

∆In_REER -7.870*** 1992 -10.043*** 1993 -5.290*** -7.629***

38 For the Republic of Congo In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

53

Gambia In_X39 -3.808** 1978*** -4.525*** 1979*** -2.332 0.545 -3.250* -2.055 0.938 -2.532

∆In_X -4.154*** -5.046*** In_M -2.810 1974*** -4.388** 1975*** -2.425 0.762 -2.810 -2.390 0.748 -2.819

∆In_M -3.840*** -6.353***

In_Y -2.735 1979*** 2000***

-3.466 1971*** 1996**

-1.480 5.790 -2.554 -1.148 8.763 -2.296

∆In_Y -6.530*** 1973 -6.901*** 1973***

1977***

-5.467*** -7.829***

In_ZY -2.937 1984***

2000***

-3.537 1982**

1995**

-2.263 4.033 -3.496** -3.128** 11.364 -3.031

∆In_ZY -6.283*** 1971*** -7.069*** 1972***

2006**

In_REER -6.123*** 1983***

2000***

-6.480*** 1984***

2000***

-0.284 -1.647 -2.028 -0.289 -1.810 -2.005

∆In_REER -4.350*** -6.159***

Mali In_X -3.096 1981*** 1998***

-3.039 1975*** 1995***

0.149 4.469 -2.440 0.552 5.804 -3.262*

∆In_X -2.823 1995 -9.233*** 2001 -5.994*** -8.900***

In_M -3.051 1981*** 1998***

-4.213 1976** 1995***

-0.621 2.905 -2.780 -0.338 3.524 -3.255*

∆In_M -5.922*** 1983 -8.087*** 1984 -5.130*** -7.971***

In_Y -2.688 1980*** 1998***

-1.333 1994** 1.025 3.584 -0.669 0.950 4.206 -0.912

∆In_Y -1.929 1977**

1985**

-7.197*** 1995* -6.958*** 1995** -4.370*** -6.446***

In_ZY40 -3.721 1980***

1996***

-3.741 1982**

1994***

-1.086 4.224 -3.334* -1.881 12.276 -3.998***

∆In_ZY -3.183 1971** -6.121*** 1972**

In_REER -5.260 1978*

1991***

-5.804*** 1985*

1992***

-0.726 -0.470 -3.077 -0.988 -0.331 -2.940

∆In_REER -6.981*** 1992 -1.128 1993 -4.676*** -7.090***

Mauritius In_X -3.497 1989***

2002***

-4.748 1984***

2003***

-0.822 2.970 -1.450 -1.143 4.248 -1.476

∆In_X -6.688*** 1983***

1988***

-7.214*** 1984***

1988***

-3.518*** -5.121***

In_M41 -5.267 1989*** 2000***

-5.066 1984*** 1995***

-0.992 1.382 -2.340 -0.856 2.103 -1.742

39 For Gambia In_X, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 40 For Mali In_ZY, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 41 For Mauritius In_M, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

54

∆In_M -5.483* 1984***

1989***

-6.474*** 1984***

1990***

-2.874** -3.443***

In_Y -2.813 1989***

2001***

-4.824*** 1983*** -0.058 4.435 -2.114 -0.220 7.862 -1.938

∆In_Y -2.917 1982* -3.896*** -5.621*** In_ZY -2.862 1989***

2001***

-1.819 1981 -0.857 4.155 -2.958 -1.252 12.655 -2.372

∆In_ZY -3.987*** 2007** -5.155*** 2006* -4.550*** -4.576*** In_REER -2.037 1981** -3.221 1985**

2008**

-1.966 0.094 -1.822 -2.115 0.118 -2.053

∆In_REER -2.546 2003 -6.295*** 2006* -3.764*** -5.851***

Mozambique In_X42 -4.951 1997**

2004**

-4.326 1992***

1998***

-0.400 1.255 -

4.664***

0.572 1.879 -3.693**

∆In_X -4.366 1997*** 2004*

-5.580*** 1985***

In_M -3.413 1996***

2006***

-2.513 1997**

2007**

-0.741 1.658 -2.643 0.874 1.564 -2.874

∆In_M -6.545*** 1983* -3.325 1984 -4.072*** -5.776***

In_Y43 -2.666 1995***

2005***

-0.068 1994** 0.701 2.219 -

5.374***

1.499 3.129 -3.466**

∆In_Y -1.247 1984*** -1.993 1985 -2.820* -3.299**

In_ZY -2.639 1990***

2001***

-1.839 1982** -0.865 4.078 -2.561 -0.752 11.811 -2.015

∆In_ZY -3.449* 2007** -6.219*** 2008 -4.674*** -4.414***

In_REER -5.567*** 1988*** -9.893*** 1983***

1985***

-1.836 -0.392 -2.455 -1.707 0.455 -2.167

∆In_REER -4.225*** -4.899***

Namibia In_X -4.400 1992*** 2003***

-4.511 1989*** 2000***

-0.550 1.794 -3.812** -0.165 1.897 -3.838**

∆In_X -2.837 1988 -5.195*** 1989

In_M44 -4.641 1997*** 2008***

-4.300 1994*** 2005***

2.432 2.438 -0.807 2.011 2.881 -1.034

∆In_M 0.203 2002 -7.391*** 2005***

2008***

-1.966 -0.774 -2.947 -3.926***

In_Y -3.388 1993***

2005***

0.179 2001 1.841 3.461 -2.671 2.661 5.813 -2.525

∆In_Y -6.139*** 1983** 2002**

-5.502*** 1984** -3.438** -4.237***

In_ZY -2.639 1990***

2001***

-1.839 1982** -0.865 4.078 -2.562 -0.751 11.811 -2.016

∆In_ZY -3.449* 2007** -6.217*** 2008 -4.674*** -4.414***

42 For Mozambique In_X, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 43 For Mozambique In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 44 For Namibia In_M, 4 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

55

In_REER45 -4.713*** 1986*** -4.942*** 1982* -2.702* -0.737 -2.269 -2.280 -0.735 -2.036

∆In_REER -3.606*** -4.593***

Senegal In_X46 -4.751 1978***

1995***

-2.528 1992*** 0.139 3.217 -2.302 -1.057 2.209 -5.192***

∆In_X -6.903*** 1978 -7.130*** 1976*** 1980***

-6.614*** -11.304***

In_M47 -3.608 1978***

2000***

-2.236 1973***

1996***

0.618 2.600 -2.539 -0.395 3.214 -3.360*

∆In_M -2.964 1975 -2.650 1976**

1980*

-4.981*** -10.612***

In_Y -2.768 1983***

2000***

-2.301 1973**

1996***

2.117 4.850 -0.795 2.303 7.899 -1.135

∆In_Y -11.586*** 1995* -11.398*** 1993*** -4.878*** -10.413***

In_ZY -3.413 1980*** 2000***

-4.404 1982** 1995***

-3.367** 3.712 -2.959 -4.716*** 10.621 -2.691

∆In_ZY -4.470 1971***

2007**

-7.374*** 1972***

2006**

In_REER -5.242*** 1991*** -5.810*** 1992*** -0.978 -0.934 -2.062 -1.136 -0.970 -2.299

∆In_REER -5.027*** -7.543***

Sierra Leone In_X -0.556 1979*** 2004***

-2.645 2011*** 0.152 0.735 0.870 0.142 0.860 1.040

∆In_X -7.797*** 2009*** -8.385*** 1994**

2011***

-3.020** -5.595***

In_M -2.858 1977***

2004***

-2.931 1998***

2009**

0.050 0.818 -0.412 -0.138 0.853 -0.444

∆In_M -4.504*** 1999*** -4.713*** 1999*** -3.688*** -6.789*** In_Y -1.709 1999***

2008***

-0.088 1990***

2000***

1.091 2.182 0.217 0.955 2.227 -0.024

∆In_Y -4.044 1989**

1999***

-6.420*** 1990***

2000***

-3.010**

-5.776***

In_ZY48 -2.986 1985*** 2000***

-3.259 1982* 1995**

-1.953 3.290 -2.842 -3.037** 11.542 -3.376*

∆In_ZY -6.859*** 1980**

2007*

-6.275*** 1972** -5.010*** -4.858***

In_REER -2.316 1982**

1987***

-4.810 1981***

1984***

-2.938** -0.309 -3.350* -2.531* -0.326 -2.810

∆In_REER -2.189 1984 -8.588*** 1979*** 1985***

-6.125*** -5.874***

45 For Namibia In_REER, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 46 For Senegal In_X, 4 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 47 For Senegal In_M and In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 48 For Sierra Leone In_ZY, 3 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

56

Togo In_X 0.460 1968***

1978***

-1.693 1969 -0.909 2.326 -1.623 -1.350 2.419 -2.183

∆In_X -0.743 1969 -9.993*** 1970 -5.316*** -8.691***

In_M49 -3.491 1972***

1978***

-2.613 1973** -1.414 1.399 -2.578 -1.058 1.581 -2.078

∆In_M -0.502 2009** -5.838*** 1976 -3.697*** -5.365***

In_Y -3.177 1974***

1998***

-5.713** 1992***

2008***

-1.981 3.317 -3.047 -2.450 4.038 -3.300*

∆In_Y -3.092 1991 -4.390*** -6.584***

In_ZY -3.413 1980***

2000***

-4.403 1982**

1995***

-3.367** 3.722 -2.959 -4.715*** 10.624 -2.691

∆In_ZY -4.470 1971***

2007**

-7.373*** 1972***

2006**

-3.877***

In_REER -2.658 1981*** 1991***

-8.130*** 1982*** 1992***

-1.408 -0.788 -1.811 -1.577 -0.916 -2.131

∆In_REER -8.741*** 1992 -12.021*** 1993 -5.972*** -8.246***

Uganda In_X -4.295 1998*** 2009***

-2.933 1993*** 2003**

0.258 3.023 -2.545 0.468 3.372 -2.832

∆In_X -2.960 2006 -7.552*** 2007 -3.920*** -6.186***

In_M50 -3.281 1996*** 2007***

0.144 1993*** -0.052 2.621 -2.506 0.178 3.357 -2.434

∆In_M -5.271*** 1993** -3.244 1994** -3.234** -3.604***

In_Y51 -2.596 1996*** 2005***

-0.798 1991** 0.378 2.934 -4.670***

1.251 7.918 -3.404**

∆In_Y -4.973*** 1987*** -2.713 1986 -3.823*** -3.105**

In_ZY -2.772 1994*** 2004***

-2.111 1994 -1.593 3.995 -2.789 -1.752 11.845 -1.990

∆In_ZY -2.802 2007** -5.160*** 2006** -4.018*** -4.373*** In_REER52 -4.972 1990***

1999*

1.270 1989 -2.809* -2.119 -1.124 -3.882*** -2.161 -3.103

∆In_REER -6.261*** 1990** -6.829*** 1991*** -3.549***

Zambia In_X -5.869*** 2000***

2006***

-3.933 1997***

2001***

2.101 2.277 0.427 2.365 2.366 0.392

∆In_X -9.247*** 1997*** 2004***

-3.103** -5.456***

In_M53 -2.603 1979**

2002***

-3.258 1973**

1997***

0.720 1.417 -0.224 1.419 1.900 0.075

49 For Togo In_M, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 50 For Uganda In_M, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 51 For Uganda In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 52 For Uganda In_REER, 4 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 53 For Zambia In_M and In_RPM2, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

57

∆In_M -6.903*** 1970*

1991***

-4.982*** 1992*** -2.089 -4.513***

In_Y -

1.239

1996***

2006***

-2.365 1994**

2003***

2.056 3.764 0.770 1.984 4.132 0.520

∆In_Y -8.567*** 2000*** -8.283*** 2001*** -3.600*** -6.639*** In_ZY -3.358 1980***

2000***

-4.399 1982**

1995***

-3.336** 3.693 -2.919 -4.645*** 10.561 -2.639

∆In_ZY -7.069*** 1971** 1980*

-7.313*** 1972*** 2006**

In_REER54 -6.444*** 1984***

2003***

-6.480*** 1985**

2003***

-0.699 0.600 -1.311 -1.385 0.441 -1.890

∆In_REER -4.030*** -5.282***

In_RPM2 -4.453 1988***

1993***

-6.164*** 1989*** -2.537* -

2.827**

-0.674 -2.184 -3.263*** -0.009

∆In_RPM2 -6.363*** 1990***

1994***

-6.243*** 1989***

1993***

In_RPM4 -4.626 1997***

2007*

1.537 1996**

2004***

-1.615 -1.107 -2.349 -2.043 -1.265 -2.947

∆In_RPM4 -5.950*** 2004 -7.866*** 2005 -5.023*** -7.912***

Zimbabwe In_X -2.741 1987***

2004***

-4.145 1978**

2000***

-1.752 0.499 -1.680 -1.675 0.405 -1.546

∆In_X -4.640 1999*** 2008***

-2.347 1998** 2007***

-3.492*** -5.496***

In_M -2.930 1987***

2010***

-1.762 1984 -1.287 1.237 -1.745 -1.418 1.210 -2.107

∆In_M -4.732 1997**

2007***

-2.643 2008* -4.539*** -7.310***

In_Y55 -3.578 1990***

2004***

-1.066 2000** -2.527 0.799 -2.291 -1.713 0.728 -1.566

∆In_Y -1.292 1999** 2006**

-7.800*** 2000*** 2007***

-2.584* -3.833***

In_ZY -2.868 1989***

2001***

-1.818 1981 -0.856 4.155 -2.959 -1.251 12.653 -2.373

∆In_ZY -3.986*** 2007** -5.156*** 2006* -4.549*** -4.577***

In_RPM2 -3.597** 1990*** -4.021 1987*** -1.233 -1.543 -1.134 -1.535 -1.714 -1.507

∆In_RPM2 -5.492** 1987** 1995***

-3.697*** -6.540***

In_RPM4 -4.058*** 1990*** -6.039*** 1983***

1987***

-2.289 -1.860 -2.513 -3.182** -2.679 -3.282*

∆In_RPM4 -4.709***

Note: The ADF unit root test uses one lagged value as determined by the presence of autocorrelation unless otherwise stated.

5% critical value for the CMR2 is -5.490

54 For Zambia In_REER, 3 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation. 55 For Zimbabwe In_Y, 2 lags were used in the Augmented Dickey fully (ADF) unit root test due to autocorrelation.

58

5% critical value for CMR1 is -3.560

5% critical value for ADF is -2.928 5% critical value for ADF no constant -1.950

5% critical value for ADF trend -3.497

5% critical value for PP is -2.927 5% critical value for PP trend -3.496

5% critical value for PP no constant -1.950

*** Indicates significance at the 99% level ** Indicates significance at the 95% level


59

Appendix D

Results from the import demand function

Results from the ARDL model

𝐾𝑒𝑛𝑦𝑎 ∆𝐼𝑛𝑀 = −2.822(1.641) − 0.347(0.103)𝐼𝑛𝑀𝑡−1 + 0.342(0.114)𝐼𝑛𝑌𝑡

− 0.519(0.211)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.260(0.085)𝐷1963𝑡𝑜78+ 0.287(0.091)𝐷1990𝑜𝑛𝑤𝑎𝑟𝑑

𝑆𝑢𝑑𝑎𝑛 ∆𝐼𝑛𝑀 = 0.035(1.338) − 0.261(0.094)𝐼𝑛𝑀𝑡−1 + 0.249(0.102)𝐼𝑛𝑌𝑡

+ 0.046(0.079)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡

𝑁𝑖𝑔𝑒𝑟𝑖𝑎 ∆𝐼𝑛𝑀= −0.636(3.835) − 0.499(0.163)𝐼𝑛𝑀𝑡−1 + 0.470(0.288)𝐼𝑛𝑌𝑡

− 0.074(0.060)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.204(0.127)∆𝐼𝑛𝑀𝑡−1 + 3.270(0.778)∆𝐼𝑛𝑌𝑡

+ 1.192(0.419)∆𝐼𝑛𝑌𝑡−1 − 0.947(0.479)∆𝐼𝑛𝑌𝑡−2 + 2.163(0.455)∆𝐼𝑛𝑌𝑡−3

+ 0.233(0.111)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.473(0.177)𝐷1988 − 0.625(0.192)𝐷1999− 1.311(0.235)𝐷2004

𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 ∆𝐼𝑛𝑀= −6.526(1.523) − 0.196(0.041)𝐼𝑛𝑀𝑡−1 + 0.407(0.072)𝐼𝑛𝑌𝑡

− 0.135(0.069)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 3.982(0.346)∆𝐼𝑛𝑌𝑡 − 0.106(0.057)𝐷1982+ 0.167(0.057)𝐷1992

𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 𝑃𝑜𝑠𝑡 𝐴𝑝𝑎𝑟𝑡ℎ𝑒𝑖𝑑 ∆𝐼𝑛𝑀= −6.417(1.517) − 0.239(0.054)𝐼𝑛𝑀𝑡−1 + 0.434(0.075)𝐼𝑛𝑌𝑡

− 0.186(0.080)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 3.763(0.403)∆𝐼𝑛𝑌𝑡 − 0.104(0.057)𝐷1982+ 0.164(0.058)𝐷1992 + 0.050(0.040)𝐷1994𝑜𝑛𝑤𝑎𝑟𝑑

𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 𝑡𝑟𝑒𝑛𝑑 ∆𝐼𝑛𝑀= −15.614(4.418) − 0.208(0.039)𝐼𝑛𝑀𝑡−1 + 0.170(0.129)𝐼𝑛𝑌𝑡

− 0.221(0.077)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 3.872(0.352)∆𝐼𝑛𝑌𝑡 − 0.091(0.055)𝐷1982+ 0.132(0.058) + 0.007(0.003)𝑡

𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 𝑃𝑜𝑠𝑡 𝐴𝑝𝑎𝑟𝑡ℎ𝑒𝑖𝑑 𝑡𝑟𝑒𝑛𝑑 ∆𝐼𝑛𝑀= −14.170(6.481) − 0.195(0.067)𝐼𝑛𝑀𝑡−1 + 0.192(0.159)𝐼𝑛𝑌𝑡

− 0.209(0.117)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 4.139(0.452)∆𝐼𝑛𝑌𝑡 − 0.389(0.444)∆𝐼𝑛𝑌𝑡−1

+ 0.058(0.106)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.008(0.120)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−1

+ 0.143(0.062)𝐷1992 + 0.004(0.053)𝐷1994𝑜𝑛𝑤𝑎𝑟𝑑 + 0.006(0.004)𝑡

𝐵𝑒𝑛𝑖𝑛 ∆𝐼𝑛𝑀 = −3.329(1.036) − 0.345(0.079)𝐼𝑛𝑀𝑡−1 + 0.394(0.086)𝐼𝑛𝑌𝑡

− 0.373(0.074)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 3.229(0.419)∆𝐼𝑛𝑌𝑡

+ 0.294(0.131)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.129(0.079)𝐷1982 − 0.144(0.074)𝐷1984+ 0.170(0.072)𝐷1992

𝐵𝑜𝑡𝑠𝑤𝑎𝑛𝑎 ∆𝐼𝑛𝑀= −1.037(0.911) − 0.954(0.196)𝐼𝑛𝑀𝑡−1 + 0.855(0.168)𝐼𝑛𝑌𝑡

− 0.508(0.216)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.828(0.173)∆𝐼𝑛𝑀𝑡−1

+ 0.094(1.154)∆𝐼𝑛𝑀𝑡−2 + 0.472(0.152)∆𝐼𝑛𝑀𝑡−3 + 0.534(0.318)∆𝐼𝑛𝑌𝑡

− 0.181(0.067)𝐷1996 − 0.196(0.069)𝐷2005 + 0.291(0.075)𝐷2012

60

𝐶𝑎𝑚𝑒𝑟𝑜𝑜𝑛 ∆𝐼𝑛𝑀= −3.735(1.504) − 0.507(0.123)𝐼𝑛𝑀𝑡−1 + 0.700(0.170)𝐼𝑛𝑌𝑡

+ 0.333(0.119)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.213(0.100)𝐷1

𝐶ℎ𝑎𝑑 ∆𝐼𝑛𝑀 = 4.976(2.946) − 0.835(0.138)𝐼𝑛𝑀𝑡−1 + 0.549(0.199)𝐼nY𝑡

− 0.233(0.145)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.218(0.129)∆𝐼𝑛𝑀𝑡−1

+ 0.715(0.111)∆𝐼𝑛𝑀𝑡−2 + 0.385(0.141)𝐷2001 + 1.080(0.144)𝐷2002

𝑅𝑒𝑝𝑢𝑏𝑙𝑖𝑐 𝑜𝑓 𝐶𝑜𝑛𝑔𝑜 𝐼𝑛𝑀 = 2.852(1.520) + 0.173(0.077)𝐼𝑛𝑀𝑡−1 − 0.258(0.110)𝐼𝑛𝑌𝑡 +0.180(0.079)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.588(0.100)∆𝐼𝑛𝑀𝑡−1 − 0.408(0.124)∆𝐼𝑛𝑀𝑡−2 +0.556(0.146)∆𝐼𝑛𝑀𝑡−3 − 0.337(0.332)∆𝐼𝑛𝑌𝑡 + 1.048(0.329)∆𝐼𝑛𝑌𝑡−1 +1.231(0.329)∆𝐼𝑛𝑌𝑡−2 − 0.964(0.350)𝐼𝑛𝑌𝑡−3 − 0.420(0.232)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 −0.167(0.219)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−1 − 0.467(0.227)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−2 − 0.999(0.231)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−3 +0.218(0.102)𝐷1980 + 0.525(0.086)𝐷1981 + 0.870(0.113)𝐷1982 +0.346(0.090)𝐷1990 + 0.854(0.081)𝐷1991 + 0.556(0.127)𝐷1993 +0.546(0.160)𝐷1994 + 0.828(0.183)𝐷1995 − 0.239(0.134)𝐷1997 −0.105(0.066)𝐷2004

𝐷𝑒𝑚𝑜𝑐𝑟𝑎𝑡𝑖𝑐 𝑅𝑒𝑝𝑢𝑏𝑙𝑖𝑐 𝑜𝑓 𝐶𝑜𝑛𝑔𝑜 ∆𝐼𝑛𝑀= −6.153(6.823) − 0.190(0.085)𝐼𝑛𝑀𝑡−1 + 0.416(0.348)𝐼𝑛𝑌𝑡

− 0.053(0.088)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.141(0.147)∆𝐼𝑛𝑀𝑡−1

− 0.215(0.124)∆𝐼𝑛𝑀𝑡−2 + 2.367(0.857)∆𝐼𝑛𝑌𝑡 − 1.285(0.975)∆𝐼𝑛𝑌𝑡−1

− 0.043(0.135)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.352(0.132)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−1

+ 0.388(0.153)𝐷1997𝑜𝑛𝑤𝑎𝑟𝑑

𝐺𝑎𝑏𝑜𝑛 ∆𝐼𝑛𝑀 = −3.618(2.052) − 0.313(0.107)𝐼𝑛𝑀𝑡−1 + 0.399(0.159)𝐼𝑛𝑌𝑡

− 0.266(0.119)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.580(0.228)∆𝐼𝑛𝑌𝑡 + 0.402(0.127)𝐷197

𝐺𝑎𝑚𝑏𝑖𝑎(𝐴𝐼𝐶) ∆𝐼𝑛𝑀= 3.343(2.166) − 0.381(0.113)𝐼𝑛𝑀𝑡−1 + 0.181(0.087)𝐼𝑛𝑌𝑡

− 0.095(0.099)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.171(0.140)∆𝐼𝑛𝑀𝑡−1

+ 0.312(0.139)∆𝐼𝑛𝑀𝑡−2 + 0.200(0.111)𝐷1977 + 0.200(0.116)𝐷1979− 0.215(0.109)𝐷1994

𝑀𝑎𝑙𝑖 ∆𝐼𝑛𝑀 = −3.102(2.648) − 0.104(0.081)𝐼𝑛𝑀𝑡−1 + 0.229(0.165)𝐼𝑛𝑌𝑡

− 0.066(0.212)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.619(0.431)∆𝐼𝑛𝑌𝑡

− 0.193(0.206)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.002(0.125)𝐷1960𝑡𝑜1992

𝑀𝑎𝑢𝑟𝑖𝑡𝑖𝑢𝑠 ∆𝐼𝑛𝑀= −1.951(1.426) − 0.179(0.064)𝐼𝑛𝑀𝑡−1 + 0.212(0.066)𝐼𝑛𝑌𝑡

− 0.203(0.229)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 2.280(0.459)∆𝐼𝑛𝑌𝑡 + 2.527(0.502)∆𝐼𝑛𝑌𝑡−1

+ 0.369(0.219)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.592(0.217)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−1

− 0.109(0.207)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−2 − 0.603(0.228)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−3

− 0.155(0.053)𝐷1982 − 0.097(0.049)𝐷1985 + 0.134(0.050)𝐷1990+ 0.150(0.052)𝐷2006

61

𝑀𝑜𝑧𝑎𝑚𝑏𝑖𝑞𝑢𝑒 ∆𝐼𝑛𝑀= 110.077(48.765) − 0.882(0.174)𝐼𝑛𝑀𝑡−1 + 1.655(0.464)𝐼𝑛𝑌𝑡

− 0.148(0.057)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 1.669(0.590)∆𝐼𝑛𝑌𝑡 + 0.724(0.324)∆𝐼𝑛𝑌𝑡−1

+ 0.203(0.083)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.290(0.095)𝐷1977𝑡𝑜1992 − 0.064(0.028)𝑡

𝑁𝑎𝑚𝑖𝑏𝑖𝑎 ∆𝐼𝑛𝑀= −6.360(1.887) − 0.281(0.101)𝐼𝑛𝑀𝑡−1 + 0.548(0.164)𝐼𝑛𝑌𝑡

− 0.041(0.175)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.761(0.494)∆𝐼𝑛𝑌𝑡 + 0.911(0.534)∆𝐼𝑛𝑌𝑡−1

+ 0.171(0.154)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.689(0.161)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−1

− 0.170(0.073)𝐷2005 + 0.148(0.065)𝐷2007

𝑆𝑒𝑛𝑒𝑔𝑎𝑙 ∆𝐼𝑛𝑀= −2.348(1.368) − 0.600(0.137)𝐼𝑛𝑀𝑡−1 + 0.665(0.146)𝐼𝑛𝑌𝑡

− 0.075(0.075)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.233(0.066)𝐷1981+ 0.039(0.032)𝐷1982𝑡𝑜1989

𝑆𝑖𝑒𝑟𝑟𝑎 𝐿𝑒𝑜𝑛𝑒 ∆𝐼𝑛𝑀= −5.053(3.802) − 0.197(0.082)𝐼𝑛𝑀𝑡−1 + 0.456(0.189)𝐼𝑛𝑌𝑡

+ 0.134(0.157)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 + 0.770(0.583)∆𝐼𝑛𝑌𝑡

+ 0.811(0.334)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.672(0.339)𝐷1986 − 0.757(0.246)𝐷1990

𝑈𝑔𝑎𝑛𝑑𝑎 ∆𝐼𝑛𝑀= 3.822(3.030) + 0.284(0.301)𝐼𝑛𝑀𝑡−1 − 0.442(0.408)𝐼𝑛𝑌𝑡

+ 0.034(0.057)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.670(0.268)∆𝐼𝑛𝑀𝑡−1

− 0.490(0.180)∆𝐼𝑛𝑀𝑡−2 − 0.376(0.175)∆𝐼𝑛𝑀𝑡−3 + 3.559(0.800)∆𝐼𝑛𝑌𝑡

+ 2.660(0.728)∆𝐼𝑛𝑌𝑡−1 + 1.193(0.640)∆𝐼𝑛𝑌𝑡−2 + 1.525(0.595)∆𝐼𝑛𝑌𝑡−3

− 0.151(0.110)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 0.700(0.115)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−1

+ 0.123(0.082)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡−2 + 0.277(0.063)𝐷1987− 0.208(0.060)𝐷1994 − 0.068(0.021)𝐷2002𝑡𝑜2006

𝑍𝑎𝑚𝑏𝑖𝑎 ∆𝐼𝑛𝑀= −12.547(4.972) − 0.166(0.124)𝐼𝑛𝑀𝑡−1 + 0.757(0.306)𝐼𝑛𝑌𝑡

− 0.044(0.015)𝐼𝑛𝑅𝑃𝑀2𝑡 − 0.288(0.198)∆𝐼𝑛𝑀𝑡−1 − 2.639(1.040)∆𝐼𝑛𝑌𝑡

− 4.526(1.216)∆𝐼𝑛𝑌𝑡−1 − 4.860(1.305)∆𝐼𝑛𝑌𝑡−2 − 3.457(1.196)∆𝐼𝑛𝑌𝑡−3

+ 0.768(0.125)∆𝐼𝑛𝑅𝑃𝑀2𝑡 + 0.151(0.104)∆𝐼𝑛𝑅𝑃𝑀2𝑡−1

+ 0.066(0.097)∆𝐼𝑛𝑅𝑃𝑀2𝑡−2 + 0.157(0.095)∆𝐼𝑛𝑅𝑃𝑀2𝑡−3

+ 0.509(0.103)∆𝐼𝑛𝑅𝑃𝑀2𝑡−4 − 0.628(0.237)𝐷1985− 0.297(0.158)𝐷1988

𝑍𝑖𝑚𝑏𝑎𝑏𝑤𝑒 ∆𝐼𝑛𝑀 = −114.102(25.102) − 0.826(0.175)𝐼𝑛𝑀𝑡−1 + 0.964(0.311)𝐼𝑛𝑌𝑡 −0.232(0.121)𝐼𝑛𝑅𝑃𝑀2𝑡 − 0.477(0.149)∆𝐼𝑛𝑅𝑃𝑀2𝑡 − 0.715(0.126)𝐷1999𝑜𝑛𝑤ard

Results from OLS

𝐷𝑒𝑚𝑜𝑐𝑟𝑎𝑡𝑖𝑐 𝑅𝑒𝑝𝑢𝑏𝑙𝑖𝑐 𝑜𝑓 𝐶𝑜𝑛𝑔𝑜 ∆𝐼𝑛𝑀= 0.039(0.031) + 2.372(0.605)∆𝐼𝑛𝑌 − 0.053(0.127)𝐼𝑛𝑖𝑅𝐸𝐸𝑅

62

𝐺𝑎𝑏𝑜𝑛, 𝑟𝑜𝑏𝑢𝑠𝑡,∆𝐼𝑛𝑀= 0.003(0.020) + 0.979(0.284)∆𝐼𝑛𝑌 − 0.178(0.221)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅+ 0.460(0.084)𝐷1974

𝑇𝑜𝑔𝑜, 𝑟𝑜𝑏𝑢𝑠𝑡, ∆𝐼𝑛𝑀 = 0.008(0.025) + 1.608(0.495)∆𝐼𝑛𝑌 − 0.834(0.203)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅

𝑈𝑔𝑎𝑛𝑑𝑎, 𝑟𝑜𝑏𝑢𝑠𝑡 ∆𝐼𝑛𝑀= −0.036(0.029) + 2.061(0.613)∆𝐼𝑛𝑌 − 0.225(0.059)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅

𝑆𝑢𝑑𝑎𝑛 ∆𝐼𝑛𝑀 = −0.007(0.036) + 0.963(0.562)∆𝐼𝑛𝑌 − 0.095(0.094)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅

𝑀𝑎𝑙𝑖 ∆𝐼𝑛𝑀 = 0.033(0.023) + 0.049(0.374)∆𝐼𝑛𝑌 − 0.099(0.169)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅+ 0.338(0.113)𝐷1978 + 0.261(0.121)𝐷1985

𝑆𝑖𝑒𝑟𝑟𝑎 𝐿𝑒𝑜𝑛𝑒 ∆𝐼𝑛𝑀= 0.018(0.037) + 0.775(0.501)∆𝐼𝑛𝑌 + 0.416(0.216)∆𝐼𝑛𝑖𝑅𝐸𝐸𝑅− 0.491(0.244)𝐷1990

Appendix E

Results from the export demand function

Results from the ARDL model

Kenya ∆InX = −1.106(1.293) − 0.077(0.083)𝐼𝑛𝑋𝑡−1

+ 0.0948 (0.090)𝐼𝑛𝑍𝑌

− 0.033(0.073)𝐼𝑛𝑅𝐸𝐸𝑅 − 0.377(0.159)∆𝐼𝑛𝑅𝐸𝐸𝑅

𝑁𝑖𝑔𝑒𝑟𝑖𝑎 ∆𝐼𝑛𝑋 = −17.597(7.200) − 0.6238(0.172)𝐼𝑛𝑋𝑡−1 + 1.041(0.333)𝐼𝑛𝑍𝑌𝑡

+ 0.021(0.074)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.388(0.210)𝐷2001

𝑆𝑢𝑑𝑎𝑛 ∆𝐼𝑛𝑋 = 3.015(1.711) − 0.094(0.039)𝐼𝑛𝑋𝑡−1 + 0.067(0.056)𝐼𝑛𝑍𝑌𝑡

− 0.648(0.110)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.131(0.137)∆𝐼𝑛𝑋𝑡−1 − 0.429(0.137)∆𝐼𝑛𝑋𝑡−2

+ 0.497(0.114)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.431(0.956)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−1

+ 0.341(0.093)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−2 + 0.334(0.086)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−3

− 0.480(0.173)𝐷1996 − 0.426(0.160)𝐷1997

𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 ∆𝐼𝑛𝑋= −1.917(1.113) − 0.067(0.035)𝐼𝑛𝑋𝑡−1 + 0.110(0.038)𝐼𝑛𝑍𝑌𝑡

+ 0.018(0.054)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 2.311(0.350)∆𝐼𝑛𝑍𝑌𝑡 − 0.126(0.060)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡

+ 0.097(0.034)𝐷1993 + 0.074(0.034)𝐷1995

𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 𝑃𝑜𝑠𝑡 𝐴𝑝𝑎𝑟𝑡ℎ𝑒𝑖𝑑 ∆𝐼𝑛𝑋= −0.778(1.337) − 0.195(0.057)𝐼𝑛𝑋𝑡−1 + 0.167(0.041)𝐼𝑛𝑍𝑌𝑡


+ 0.070(0.029)𝐷1994𝑜𝑛𝑤𝑎𝑟𝑑

63

𝐵𝑒𝑛𝑖𝑛 ∆𝐼𝑛𝑋 = −32.684(15.866) − 0.505(0.219)𝐼𝑛𝑋𝑡−1 + 1.351(0.620)𝐼𝑛𝑍𝑌𝑡

+ 0.029(0.234)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.648(0.262)∆𝐼𝑛𝑋𝑡−1 − 0.009(0.237)∆𝐼𝑛𝑋𝑡−2

+ 0.488(0.256)∆𝐼𝑛𝑋𝑡−3 − 0.327(0.257)∆𝐼𝑛𝑋𝑡−4 + 0.631(0.259)∆𝐼𝑛𝑋𝑡−5

+ 1.524(2.425)∆𝐼𝑛𝑍𝑌𝑡 + 2.173(2.678)∆𝐼𝑛𝑍𝑌𝑡−1 + 1.023(2.743)∆𝐼𝑛𝑍𝑌𝑡−2

+ 2.827(3.010)∆𝐼𝑛𝑍𝑌𝑡−3 + 1.327(2.744)∆𝐼𝑛𝑍𝑌𝑡−4

+ 3.944(3.513)∆𝐼𝑛𝑍𝑌𝑡−5 + 1.283(3.090)∆𝐼𝑛𝑍𝑌𝑡−6

− 0.707(0.549)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.078(0.565)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−1

− 0.432(0.516)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−2 − 0.497(0.457)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−3

− 0.664(0.482)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−4 − 0.278(0.414)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−5

𝐵𝑜𝑡𝑤𝑎𝑛𝑎 ∆𝐼𝑛𝑋= −10.767(3.508) − 0.338(0.108)𝐼𝑛𝑋𝑡−1 + 0.656(0.208)𝐼𝑛𝑍𝑌𝑡

− 0.534(0.305)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 6.345(1.337)∆𝐼𝑛𝑍𝑌𝑡 + 0.275(0.110)𝐷1982+ 0.274(0.102)𝐷1983

𝐶𝑎𝑚𝑒𝑟𝑜𝑜𝑛 ∆𝐼𝑛𝑋= −2.982(2.904) − 0.162(0.065)𝐼𝑛𝑋𝑡−1 + 0.218(0.117)𝐼𝑛𝑍𝑌𝑡

− 0.080(0.111)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.254(0.146)∆𝐼𝑛𝑋𝑡−1 + 2.289(1.131)∆𝐼𝑛𝑍𝑌𝑡

+ 0.301(0.103)𝐷1980 + 0.324(0.105)𝐷1981 + 0.399(0.105)𝐷1984+ 0.235(0.116)𝐷1985

𝐶ℎ𝑎𝑑 ∆𝐼𝑛𝑋 = −28.323(17.026) − 0.455(0.179)𝐼𝑛𝑋𝑡−1 + 1.124(0.549)𝐼𝑛𝑍𝑌𝑡

+ 0.574(0.428)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 9.010(4.291)∆𝐼𝑛𝑍𝑌𝑡 − 7.294(4.291)∆𝐼𝑛𝑍𝑌𝑡−1

− 0.504(0.301)𝐷1982

𝐷𝑒𝑚𝑜𝑐𝑟𝑎𝑡𝑖𝑐 𝑅𝑒𝑝𝑢𝑏𝑙𝑖𝑐 𝑜𝑓 𝐶𝑜𝑛𝑔𝑜 ∆𝐼𝑛𝑋= −11.181(3.787) − 0.155(0.074)𝐼𝑛𝑋𝑡−1 + 0.441(0.132)𝐼𝑛𝑍𝑌𝑡


− 0.341(0.109)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−1 − 0.410(0.183)𝐷1997

𝑅𝑒𝑝𝑢𝑏𝑙𝑖𝑐 𝑜𝑓 𝐶𝑜𝑛𝑔𝑜 (𝐴𝐼𝐶) ∆𝐼𝑛𝑋= −2.490(1.708) − 0.372(0.086)𝐼𝑛𝑋𝑡−1 + 0.379(0.105)𝐼𝑛𝑍𝑌𝑡

− 0.225(0.068)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.378(0.126)∆𝐼𝑛𝑋𝑡−1 − 0.013(0.632)∆𝐼𝑛𝑍𝑌𝑡

− 0.877(0.607)∆𝐼𝑛𝑍𝑌𝑡−1 − 0.976(0.628)∆𝐼𝑛𝑍𝑌𝑡−2 + 0.172(0.557)𝐷1980− 0.184(0.060)𝐷1994 − 0.201(0.055)𝐷2007

𝐺𝑎𝑚𝑏𝑖𝑎 (𝐴𝐼𝐶) ∆𝐼𝑛𝑋 = −9.292(3.974) − 0.409(0.087)𝐼𝑛𝑋𝑡−1 + 0.490(0.137)𝐼𝑛𝑍𝑌𝑡 +0.357(0.126)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.340(0.116)∆𝐼𝑛𝑋𝑡−1 + 0.216(0.127)∆𝐼𝑛𝑋𝑡−2 −2.215(1.308)∆𝐼𝑛𝑍𝑌𝑡 − 0.278(0.218)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.245(0.111)𝐷1994 −0.391(0.126)𝐷2006

𝑀𝑎𝑙𝑖 ∆𝐼𝑛𝑋 = −13.637(6.445) − 0.410(0.103)𝐼𝑛𝑋𝑡−1 + 0.759(0.267)𝐼𝑛𝑍𝑌𝑡

− 0.353(0.095)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.473(0.150)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡

+ 0.503(0.133)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−1 − 0.565(0.199)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−2

− 0.424(0.123)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−3 − 0.185(0.076)𝐷1978 + 0.364(0.083)𝐷1980− 0.493(0.113)𝐷1996 + 0.118(0.069)𝐷2001

64

𝑀𝑎𝑢𝑟𝑖𝑡𝑖𝑢𝑠 ∆𝐼𝑛𝑋= −2.318(3.065) − 0.098(0.085)𝐼𝑛𝑋𝑡−1 + 0.155(0.576)𝐼𝑛𝑍𝑌𝑡

− 0.080(0.179)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.868(0.789)∆𝐼𝑛𝑍𝑌𝑡 − 0.044(0.255)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡

− 0.108(0.067)𝐷1981 − 0.010(0.062)𝐷2000 + 0.110(0.060)𝐷2001− 0.153(0.061)𝐷2002 − 0.090(0.058)𝐷2003

𝑀𝑜𝑧𝑎𝑚𝑏𝑖𝑞𝑢𝑒 ∆𝐼𝑛𝑋= −25.351(11.402) − 0.199(0.076)𝐼𝑛𝑋𝑡 + 0.956(0.406)𝐼𝑛𝑍𝑌𝑡

− 0.089(0.058)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 0.181(0.089)𝐷1992 + 0.242(0.086)𝐷2001

𝑁𝑎𝑚𝑖𝑏𝑖𝑎 ∆𝐼𝑛𝑋= −18.072(3.631) − 0.911(0.157)𝐼𝑛𝑋𝑡−1 + 1.184(0.204)𝐼𝑛𝑍𝑌𝑡

+ 0.170(0.136)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 + 0.537(0.186)∆𝐼𝑛𝑋𝑡−1 − 2.238(0.949)∆𝐼𝑛𝑍𝑌𝑡

− 1.211(0.959)∆𝐼𝑛𝑍𝑌𝑡−1 − 0.411(0.165)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡

− 0.082(0.177)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡−1 − 0.237(0.060)𝐷1990 − 0.135(0.078)𝐷1992− 0.156(0.060)𝐷2001

𝑆𝑒𝑛𝑒𝑔𝑎𝑙 ∆𝐼𝑛𝑋= 2.672(2.790) − 0.858(0.126)𝐼𝑛𝑋𝑡−1 + 0.520(0.123)𝐼𝑛𝑍𝑌𝑡

− 0.085(0.108)𝐼𝑛𝑖𝑅𝐸𝐸𝑅𝑡 − 1.800(1.029)∆𝐼𝑛𝑍𝑌𝑡 − 2.187(0.951)∆𝐼𝑛𝑍𝑌𝑡−1

− 2.671(1.025)∆𝐼𝑛𝑍𝑌𝑡−2 − 0.252(0.085)𝐷1980 − 0.188(0.086)𝐷1991− 0.252(0.089)𝐷1992 − 0.358(0.092)𝐷1993

𝑈𝑔𝑎𝑛𝑑𝑎 ∆𝐼𝑛𝑋= −32.786(14.364) − 0.374(0.113)𝐼𝑛𝑋𝑡−1 + 1.298(0.512)𝐼𝑛𝑍𝑌𝑡

− 0.004(0.105)𝐼𝑛𝑅𝐸𝐸𝑅𝑡 − 4.156(2.293)∆𝐼𝑛𝑍𝑌𝑡 + 0.168(0.168)∆𝐼𝑛𝑅𝐸𝐸𝑅𝑡

− 0.267(0.157)𝐷1991 − 0.311(0.160)𝐷1993

𝑍𝑎𝑚𝑏𝑖𝑎 ∆𝐼𝑛𝑋 = −11.185(5.327) − 0.051(0.031)𝐼𝑛𝑋𝑡−1 + 0.411(0.183)𝐼𝑛𝑍𝑌𝑡

− 0.520(0.143)𝐼𝑛𝑅𝑃𝑋4𝑡 − 1.002(0.284)∆𝐼𝑛𝑋𝑡−1 + 1.013(2.086)∆𝐼𝑛𝑍𝑌𝑡

− 6.524(2.019)∆𝐼𝑛𝑍𝑌𝑡−1 + 0.462(0.122)∆𝐼𝑛𝑅𝑃𝑋4𝑡

+ 0.110(0.112)∆𝐼𝑛𝑅𝑃𝑋4𝑡−1 + 0.332(0.178)𝐷2000 + 0.247(0.133)𝐷2003+ 0.328(0.140)𝐷2004 + 0.323(0.147)𝐷2005

𝑍𝑖𝑚𝑏𝑎𝑏𝑤𝑒 ∆𝐼𝑛𝑋= 224.114(80.509) − 0.526(0.113)𝐼𝑛𝑋𝑡−1 + 7.697(2.971)𝐼𝑛𝑍𝑌𝑡

− 0.732(0.217)𝐼𝑛𝑅𝑃𝑋4𝑡 + 0.639(0.213)∆𝐼𝑛𝑋𝑡−1 + 0.385(0.220)∆𝐼𝑛𝑋𝑡−2

+ 0.656(0.187)∆𝐼𝑛𝑋𝑡−3 − 6.335(2.255)∆𝐼𝑛𝑍𝑌𝑡 + 0.840(0.238)∆𝐼𝑛𝑅𝑃𝑋4𝑡

+ 0.608(0.214)∆𝐼𝑛𝑅𝑃𝑋4𝑡−1 + 0.327(0.151)∆𝐼𝑛𝑅𝑃𝑋4𝑡−2

+ 0.305(0.120)∆𝐼𝑛𝑅𝑃𝑋4𝑡−3 + 0.192(0.106)𝐷2001 + 0.311(0.161)𝐷2004− 0.333(0.140)𝐷2007 − 0.481(0.135)𝐷2008 − 0.226(0.085)𝑡

Results from OLS

𝐷𝑒𝑚𝑜𝑐𝑟𝑎𝑡𝑖𝑐 𝑅𝑒𝑝𝑢𝑏𝑙𝑖𝑐 𝑜𝑓 𝐶𝑜𝑛𝑔𝑜 ∆𝐼𝑛𝑋= −0.122(0.073) + 3.972(1.793)∆𝐼𝑛𝑍𝑌 − 0.066(0.111)∆𝐼𝑛𝑅𝐸𝐸𝑅+ 0.118(0.060)𝐷1997𝑜𝑛𝑤𝑎𝑟𝑑

𝐺𝑎𝑏𝑜𝑛 ∆𝐼𝑛𝑋 = −0.018(0.037) + 1.781(0.988)∆𝐼𝑛𝑍𝑌 − 0.071(0.201)∆𝐼𝑛𝑅𝐸𝐸𝑅+ 0.231(0.123)𝐷1975 − 0.178(0.111)𝐷2000

65

Appendix F

Results: Import demand function controlling for Apartheid South Africa

Long run

The

income

elasticity

of demand

for

imports, π

The price

elasticity

of demand

for

imports, ψ ARDL SBC R2

Adjusted

R2

Bounds F

test

Breusch-

Pagan/Cook-

Weisberg test for

heteroscedasticity

(P value)

Breusch-

Godfrey

test for

serial

correlation

(P value)

Ramsey

regression

specification-

error test for

omitted

variables (P

value)

South Africa 2.077*** (0.264) -0.691* (0.375) (1 1 0) -129.922 0.781 0.751 12.078*** 0.702 0.155 0.335

South Africa

(trend)

0.955* (0.548) -1.080* (0.555) (1 2 2) -126.727 0.791 0.746 4.496 0.522 0.116 0.601

South Africa

(trend )

0.819 (0.59) -1.064 (0.399) (1 1 0) -131.366 0.803 0.77 10.590*** 0.776 0.263 0.535

South Africa

Post-Apartheid56

1.811 (0.263) -0.776* (0.313) (1 1 0) -127.77 0.789 0.753 12.110*** 0.746 0.153 0.414

South Africa

Post-Apartheid

(trend)

0.981 (0.641) -1.072* (0.561) (1 2 2) -122.783 0.791 0.74 3.136 0.525 0.108 0.5994




56 For South Africa, we estimate the import demand function using two different specifications; in the second specification we control for apartheid by including a dummy

variable which takes the value of 1 for the period 1994 onwards and zero otherwise. We include a trend as unit root tests provided evidence that some of the variables are

trend stationary.

66

For South Africa we use the Wald test to formally determine if the income and price elasticities

are statistically significantly different for the specification that controls for apartheid and that

which does not. The two estimates for the income elasticities of demand are 2.077 for the

former and 1.811 for the latter. The F statistic and P value from the Wald test (H0: 2.077=1.811)

were, 1.01 and 0.319 respectively. The two estimates for the price elasticities are -0.691 and -

0.776 receptively. The F statistic and P value from the Wald test (H0:-0.691= -0.776) were,

0.05 and 0.821 respectively. The results from the unit root tests indicated that the South African

GDP series is trend stationary. We therefore modify to include a trend and test if the two

specifications differ. We test if the income and price elasticities of demand are statistically

different from each other. The two respective income elasticities of demand were 0.819 and

0.981 respectively. The F statistic and P value from the Wald test (H0:0.819=0.981) were 0.07

and 0.786 respectively while the price elasticities of demand were -1.064 and -1.072

respectively. The corresponding F statistic and P value from the Wald test (H0: -1.064= -1.072)

were 0.00 and 0.983 respectively. We also test if the specification with a trend differs from the

specification without a trend without controlling for apartheid, the income elasticities were

2.077 and 0.819. The F statistic and P value from the Wald test (H0: 0.819=2.077) were 4.54

and 0.039. The price elasticities of demand were -0.691 and -1.064. The F statistic and P value

for the Wald test (H0: -1.064=-0.691) were 0.87 and 0.357. We therefore continue with the

specification which includes a trend but does not control for apartheid.

67

Export demand function controlling for Apartheid

The

income

elasticity

of demand

for

exports, ε

The

price

elasticity

of

demand

for

exports,

η ARDL SBC R2

Adjusted

R2 Bounds F test

Breusch-

Pagan/Cook-

Weisberg test for

heteroscedasticity

P value

Breusch-

Godfrey

test for

serial

correlation

P value

Ramsey

regression

specification-

error test for

omitted

variables

P value

South

Africa

1.637** (0.629) 0.268 (0.839) (1 1 1) -175.118 0.598 0.531 6.253** 0.095* 0.234 0.015**

South

Africa

Post-

Apartheid57

0.854*** (0.20) 0.317 (0.306) (1 1 1) -172.898 0.545 0.482 6.415*** 0.086* 0.752 0.049**




57 For South Africa, we test if the income and price elasticities of demand for exports differs when controlling for apartheid using the Wald test. The income elasticity of

demand was 1.637 and 0.854 when controlling for apartheid. The F statistic and P value were 1.55 and 0.220 respectively. The price elasticity of demand was 0.268 and

0.317 when controlling for apartheid. The F statistic and P value were 0.00 and 0.954 respectively. We therefore continue with the specification which does not control for

apartheid.

68

Appendix G

The balance of payments constrained growth rate for the sub periods 1960-1980

Average Start

Period Country Actual 𝑦𝐵 ∗ 𝑦𝐵 𝑦𝐵𝑆𝐷𝐴 𝑦𝐵𝑆𝐷𝐴𝑅 ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇 𝑦𝐵𝑆𝐷𝐴 𝑦𝐵𝑆𝐷𝐴𝑅 ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇

1960-1980 Sudan 2.911 3.458 2.187 3.433 2.382 -10.092 3.935 3.443 2.455 -9.913 4.122

1960-1980 Sudan (OLS) 2.911 3.437 3.416 2.369 3.914 3.424 2.441 4.099

1960-1980 Kenya 6.77 4.284 5.962 4.292 1.155 3.273 1.277 4.304 2.912 4.870 3.044

1960-1980 Benin 3.02 10.625 11.300 8.610 7.937 9.278 8.724 8.681 8.353 9.675 9.120

1960-1980 Cameroon 4.705 4.227 4.173 2.721 -0.811 3.589 4.207 3.649 0.177 4.473

1960-1980 Chad -0.408 3.446 26.566 26.801 0.635 28.059 15.906 15.841 0.352 16.542

1960-1980 Congo, Dem.

Rep.

2.026 1.540 6.274 1.888 -0.469 6.051 -0.091 2.299 1.737 9.164 1.998

1960-1980 Congo, Dem.

Rep.58 (OLS)

2.026 1.415 8.089 1.762 -0.436 8.679 -0.085 2.187 1.651 12.352 1.899

1960-1980 Congo, Rep. 5.686 9.328 3.314 10.350 9.626 2.792 9.732 6.273 5.502 1.532 5.730

1960-1980 Gabon 8.504 9.403 10.580 10.417 10.232 10.638 10.405 10.486

1960-1980 Gabon (OLS) 8.504 12.246 8.781 12.112 11.654 8.875 12.300 12.106 11.860 8.997 12.469

1966-1980 Gambia 5.224 9 11.374 -32.518 -26.543 -19.818 -15.844 -13.795 -13.523 -9.843 -8.105

1967-1980 Mali 4.309 4.012 3.806 2.212 2.046 4.401 5.814 1.851 1.712 4.502 5.684

1960-1980 Senegal 2.014 2.474 2.642 2.421 1.378 2.096 1.926 2.410 2.214 2.934 2.769

1967-1980 Sierra Leone 3.526 -1.382 -1.322 -1.543 -2.644 -1.226 -1.328 -2.478

1960-1980 Togo 6.741 10.088 8.078 7.666 7.690 6.309 6.074 6.103

1960-1980 Zambia 2.816 0.315 8.509 0.215 -1.343 4.604 -1.544 0.214 -0.301 5.277 -0.490 Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio. Average refers to the average value for these two ratios






∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments abroad and the terms of trade interacted with the price elasticities of demand


𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments and the terms of trade (only the income and price elasticities from the import



58 Both the export and import demand function are estimated with OLS.

69

The balance of payments constrained growth rate for the sub periods 1980-2014

Average Start

Period Country Actual 𝑦𝐵 ∗ 𝑦𝐵 𝑦𝐵𝑆𝐷𝐴 𝑦𝐵𝑆𝐷𝐴𝑅 ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇 𝑦𝐵𝑆𝐷𝐴 𝑦𝐵𝑆𝐷𝐴𝑅 ∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇

1980-2014 Kenya 3.786 4.480 3.616 4.484 6.599 4.443 5.677 4.484 7.092 4.790 6.110

1980-2014 South Africa 2.357 3.218 4.981 3.205 3.041 4.903 3.087 3.205 3.041 4.929 3.119

1980-2012 Sudan 4.642 7.485 2.180 7.520 5.004 -45.990 13.701 7.611 -2.360 -55.923 9.474

1980-2014 Sudan (OLS) 4.642 7.439 7.468 4.969 13.604 7.546 -2.338 9.383

1980-2014 Benin 4.172 5.542 6.792 5.163 4.939 6.270 5.051 4.513 4.283 5.517 4.456

1980-2014 Cameroon 3.148 3.236 3.295 3.600 -0.293 3.244 3.411 3.905 -0.234 3.572

1980-2005 Chad 6.955 23.745 90.000 94.035 -26.061 69.232 164.423 166.438 -47.811 118.928

1980-2014 Congo, Dem. Rep. 0.998 3.979 2.718 4.409 2.213 0.386 1.870 4.371 -2.072 -4.097 -2.458

1980-2014 Congo, Dem. Rep.

(OLS)

0.998 3.655 3.504 4.081 2.039 1.545 1.723 4.043 -1.891 -2.437 -2.242

1980-2014 Congo, Rep. 3.956 2.790 1.992 3.368 2.781 1.932 2.209 3.442 2.816 2.013 2.297

1980-2014 Gabon 2.284 1.152 1.303 0.830 0.718 1.253 0.588 0.440

1980-2014 Gabon (OLS) 1.500 5.281 1.483 0.949 3.983 0.091 1.488 0.705 3.494 -0.482

1980-2013 Gambia 3.595 8.951 7.354 30.827 41.508 -41.249 -7.233 -5.411 -4.843 10.567 6.683

1980-2007 Mali 3.607 3.672 2.672 2.421 2.304 0.921 1.029 2.002 1.926 0.476 0.565

1980-2014 Senegal 3.384 3.577 1.588 3.425 3.299 -0.319 1.696 3.375 3.153 -0.736 1.331

1980-2014 Sierra Leone 3.09 5.929 4.635 3.372 4.347 3.787 2.850 3.903

1980-2014 Togo 2.437 2.611 2.125 1.689 1.581 2.160 1.580 1.472

1980-2013 Zambia 3.835 3.075 5.139 2.725 0.215 3.338 1.201 2.380 0.246 3.058 1.238 Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio. Average refers to the average value for these two ratios






∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments abroad and the terms of trade interacted with the price elasticities of demand


𝑦𝐵𝑆𝐷𝐴𝑅𝑇𝑂𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments and the terms of trade (only the income and price elasticities from the import



70

Appendix H

59 For Sudan import and export demand function from ARDL.

Results from the Wald test for the equality of the estimated income elasticity of demand, �̂�, and the hpothetical income elsasticity of demand, 𝜋𝐻 , 1960 − 1980 Period Country �̂� 𝜋𝐻𝐵 ∗ 𝜋𝐻𝐵 𝜋𝐻𝐵𝑆𝐷𝐴 𝜋𝐻𝐵𝑆𝐷𝐴𝑅 ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴 𝜋𝐻𝐵𝑆𝐷𝐴𝑅 ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇

1960-

1980

Kenya 0.986 0.624 0.868 0.664 0.372 0.603 0.385 0.716 0.596 0.794 0.610

F statistic 2.62 0.31 2.29 8.34*** 3.25* 7.99*** 1.61 3.37* 0.82 3.13*

P value 0.112 0.581 0.137 0.006 0.078 0.007 0.210 0.073 0.371 0.083

1964-

1980

Sudan59 0.957 1.137 0.719 1.164 0.755 -4.002 1.348 1.152 0.795 -3.598 1.387

F statistic 0.83 1.46 1.10 1.05 633.17*** 3.93** 0.97 0.68 534.2*** 4.75**

P Value 0.367 0.232 0.300 0.309 0.000 0.053 0.328 0.414 0.000 0.034

1964-

1980

Sudan

(OLS) 0.963 1.137 1.164 0.755 1.348 1.152 0.795 1.387

F statistic 0.09 0.13 0.14 0.47 0.11 0.09 0.57

P Value 0.759 0.723 0.711 0.497 0.739 0.765 0.455

1960-

1980

Benin 1.142 4.017 4.273 2.047 1.928 2.142 2.054 2.077 2.018 2.235 2.143

F statistic 691.44*** 820.09*** 68.45*** 52.63*** 83.59*** 69.52*** 73.07*** 64.23*** 99.87*** 83.76***

P Value 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1960-

1980

Cameroon 1.379 1.239 1.228 0.845 1.079 1.235 1.079 1.313

F statistic 2.57 2.99 37.12*** 11.74*** 2.72 11.74 0.58

P Value 0.117 0.092 0.000 0.001 0.107 0.001 0.452

1960-

1980

Chad 0.656 -5.541 -1.459 -1.411 0.576 -1.506 -1.623 -1.574 0.551 -1.670

F statistic 1555*** 181.32*** 173.19*** 0.27 189.47 210.52*** 201.57 0.45 219.29***

P Value 0.000 0.000 0.000 0.610 0.000 0.000 0.000 0.506 0.000

1960-

1980

Congo,

Dem. Rep. 2.179 1.656 6.748 1.996 -0.958 7.240 -0.483 2.685 1.653 15.187 2.129

F statistic 0.17 13.01*** 0.02 6.13** 15.97*** 4.42** 0.16 0.17 105.47*** 0.00

P Value 0.682 0.001 0.885 0.018 0.000 0.042 0.619 0.680 0.000 0.968

71

60 For Gabon both the import and export demand function are estimated using OLS.

1960-

1980

Congo,

Dem. Rep.

(OLS) 2.372 1.657 9.471 1.996 -0.958 11.371 -0.483 2.685 1.653 22.172 2.129

F statistic 1.40 137.54*** 0.39 30.28*** 221.02*** 22.26*** 0.27 1.41 1070.04*** 0.16

P Value 0.243 0.000 0.536 0.000 0.000 0.000 0.608 0.240 0.000 0.689

1960-

1980

Congo,

Rep. 1.483 2.433 0.864 3.056 2.778 0.532 2.813 1.574 1.455 0.852 1.489

F statistic 10.61*** 4.51** 29.09*** 19.71*** 10.65*** 20.79*** 0.10 0.01 4.69** 0.00

P Value 0.005 0.049 0.000 0.000 0.004 0.000 0.760 0.923 0.045 0.984

1960-

1980

Gabon 1.275 1.409 1.846 1.717 1.740 1.888 1.814 1.837

F statistic 0.74 13.52*** 8.09*** 8.96*** 15.58** 12.04*** 13.10***

P Value 0.395 0.000 0.006 0.004 0.000 0.001 0.000

1960-

1980

Gabon60

(OLS) 0.979 1.409 1.010 1.846 1.717 1.045 1.869 1.888 1.814 1.101 1.966

F statistic 2.28 0.01 9.29*** 6.73*** 0.05 9.79*** 10.21*** 8.61*** 0.18 12.04***

P Value 0.137 0.915 0.003 0.012 0.819 0.003 0.002 0.005 0.673 0.001

1966-

1980

Gambia 0.475 0.818 1.034 0.916 0.858 0.777 0.729 0.927 0.921 0.834 0.792

F statistic 3.13* 8.32*** 5.18** 3.91** 2.43 1.72 5.44** 5.30** 3.43* 2.68

P Value 0.085 0.006 0.029 0.056 0.128 0.198 0.025 0.027 0.072 0.110

1967-

1980

Mali 2.195 2.043 1.939 1.418 1.361 2.228 2.749 1.331 1.287 2.262 2.675

F statistic 0.02 0.06 0.53 0.61 0.00 0.27 0.65 0.72 0.00 0.20

P Value 0.887 0.812 0.473 0.441 0.975 0.608 0.425 0.402 0.950 0.657

1960-

1980

Senegal 1.107 1.359 1.452 1.294 0.823 1.143 1.068 1.282 1.195 1.512 1.439

F statistic 9.60*** 18.01*** 5.28** 12.28*** 0.19 0.24 4.62** 1.16 24.83*** 16.18***

P Value 0.003 0.000 0.027 0.001 0.664 0.629 0.038 0.287 0.000 0.000

1967-

1980

Sierra

Leone 2.31 -0.905 -0.764 -0.865 -1.555 -0.557 -0.601 -1.291

F statistic 10.82*** 9.89*** 10.55*** 15.64*** 8.61*** 8.87*** 13.57***

P Value 0.002 0.003 0.002 0.000 0.005 0.005 0.000

72

1960-

1980

Togo

(OLS) 1.608 2.406 1.848 1.772 1.777 1.544 1.510 1.514

F statistic 2.59 0.23 0.11 0.10 0.02 0.04 0.03

P Value 0.114 0.632 0.743 0.752 0.897 0.843 0.859

1960-

1980

Zambia 4.562 0.510 13.786 0.692 -1.077 6.987 -1.329 0.693 0.070 8.108 -0.202

F statistic 3.49* 18.08*** 3.18* 6.76** 1.25 7.37** 3.18* 4.29* 2.67 4.82**

P Value 0.084 0.001 0.097 0.022 0.283 0.017 0.097 0.058 0.126 0.046 Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio. Average refers to the average value for these two ratios






∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation, interest payments abroad and the terms

of trade interacted with the price elasticities of demand for imports and exports

𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation, interest payments and the terms of trade

(only the income and price elasticities from the import demand function are included)




Results from the Wald test for the equality of the estimated income elasticity of demand, �̂�, and the hpothetical income elsasticity of demand, 𝜋𝐻 , 1980 − 2014

Average Start

Period Country �̂� 𝜋𝐻𝐵 ∗ 𝜋𝐻𝐵 𝜋𝐻𝐵𝑆𝐷𝐴 𝜋𝐻𝐵𝑆𝐷𝐴𝑅 ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴 𝜋𝐻𝐵𝑆𝐷𝐴𝑅 ∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇

1980-

2014

Kenya 0.986 1.166 0.941 1.157 1.471 1.099 1.312 1.158 1.521 1.148 1.362

F statistic 0.72 0.04 0.65 5.21** 0.28 2.35 0.65 6.33** 0.58 3.13*

P value 0.401 0.833 0.425 0.027 0.597 0.132 0.422 0.015 0.450 0.083

1980-

2014

South Africa 0.955 1.304 2.018 1.344 1.246 2.089 1.280 1.333 1.251 2.068 1.284

F statistic 0.40 3.75** 0.50 0.28 4.27** 0.35 0.47 0.29 4.11** 0.36

P Value 0.528 0.059 0.482 0.598 0.045 0.557 0.494 0.592 0.049 0.552

1980-

2014

Sudan 0.957 1.543 0.449 1.493 1.023 -8.216 2.598 1.397 0.025 -7.106 1.600

F statistic 8.83*** 6.65*** 5.34** 0.11 2166*** 69.29*** 4.97** 22.38*** 1673*** 10.63***

P Value 0.004 0.013 0.025 0.740 0.000 0.000 0.030 0.000 0.000 0.002

73

61 For Gabon both the import and export demand function are estimated using OLS.

1980-

2014

Sudan (OLS) 0.963 1.543 1.493 1.023 2.598 1.397 0.025 1.600

F statistic 1.06 0.89 0.01 8.44*** 0.59 2.79 1.28

P Value 0.308 0.351 0.916 0.005 0.444 0.101 0.263

1980-

2014

Benin 1.142 1.517 1.859 1.325 1.277 1.512 1.297 1.182 1.154 1.295 1.174

F statistic 11.73*** 42.95*** 2.79* 1.51 11.42*** 2.00 0.13 0.01 1.94 0.08

P Value 0.001 0.000 0.105 0.228 0.002 0.168 0.720 0.917 0.173 0.775

1980-

2014

Cameroon 1.379 1.417 1.446 1.572 -0.096 1.420 1.513 1.726 -0.170 1.573

F statistic 0.18 0.57 4.80** 282.75** 0.21 2.31 15.57*** 311.82*** 4.85**

P Value 0.673 0.454 0.034 0.000 0.648 0.137 0.000 0.000 0.033

1980-

2014

Chad 0.656 2.239 1.515 1.507 0.333 1.264 1.471 1.470 0.376 1.227

F statistic 101.36*** 29.81*** 29.26*** 4.25** 14.92*** 26.84*** 26.77*** 3.20* 13.16***

P Value 0.000 0.000 0.000 0.049 0.000 0.000 0.000 0.085 0.001

1980-

2012

Congo, Dem.

Rep. 2.179 8.688 5.935 10.379 4.929 0.794 4.153 10.218 -4.005 -8.083 -4.081

F statistic 26.41*** 8.79*** 41.91*** 4.71** 1.20 2.43 40.28*** 23.84*** 65.64*** 24.43***

P Value 0.000 0.005 0.000 0.036 0.281 0.127 0.000 0.000 0.000 0.000

1980-

2012

Congo, Dem.

Rep.(OLS) 2.372 8.688 8.330 10.379 4.929 3.716 4.153 10.218 -4.005 -5.211 -4.781

F statistic 108.87*** 96.87*** 174.97*** 17.84*** 4.93** 8.65*** 168.01*** 111.02*** 156.98*** 139.68***

P Value 0.000 0.000 0.000 0.000 0.031 0.005 0.000 0.000 0.000 0.000

1980-

2014

Congo, Rep. 1.483 1.046 0.746 1.097 0.746 0.213 0.387 1.110 0.694 0.138 0.335

F statistic 2.25 6.40** 1.76 6.40** 18.98*** 14.14*** 1.64 7.33** 21.19*** 15.51***

P Value 0.153 0.022 0.203 0.022 0.000 0.001 0.218 0.015 0.000 0.001

1980-

2014

Gabon 1.275 0.643 0.226 -0.225 -0.341 0.429 -0.049 -0.165

F statistic 16.64*** 45.81*** 93.63*** 108.67*** 29.81*** 72.96*** 86.30***

P Value 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1980-

2014

Gabon61 (OLS) 0.979 0.634 2.263 0.226 -0.225 2.513 -1.00 0.429 -0.049 1.767 -0.823

F statistic 1.48 20.38 7.03*** 17.95*** 29.78*** 48.48*** 3.75* 13.09*** 7.67*** 40.20

P Value 0.230 0.000 0.010 0.000 0.000 0.000 0.058 0.000 0.008 0.000

74

1980-

2013

Gambia 0.475 1.183 0.971 1.111 1.076 -0.236 0.303 1.054 1.041 0.008 0.268

F statistic 13.35*** 6.55** 10.77*** 9.62*** 13.46*** 0.79 8.93*** 8.53*** 5.81** 1.14

P Value 0.000 0.015 0.002 0.003 0.000 0.380 0.005 0.006 0.021 0.292

1980-

2007

Mali 2.195 2.235 1.626 1.633 1.588 0.944 0.995 1.487 1.462 0.829 0.868

F statistic 0.00 0.28 0.28 0.32 1.37 1.26 0.44 0.47 1.63 1.54

P Value 0.970 0.598 0.603 0.574 0.251 0.271 0.513 0.498 0.211 0.224

1980-

2014

Senegal 1.107 1.170 0.519 1.116 1.088 0.288 0.734 1.105 1.062 0.305 0.707

F statistic 0.59 52.55*** 0.01 0.06 101.91*** 21.17*** 0.00 0.31 97.72*** 24.34***

P Value 0.446 0.000 0.916 0.811 0.000 0.000 0.975 0.578 0.000 0.000

1980-

2014

Sierra Leone 2.31 4.433 3.300 2.482 3.080 2.718 2.174 2.771

F statistic 4.71** 1.02 0.03 0.62 0.17 0.02 0.22

P Value 0.036 0.318 0.862 0.436 0.679 0.889 0.640

1980-

2014

Togo (OLS) 1.608 1.723 1.450 1.237 1.183 1.465 1.178 1.124

F statistic 0.05 0.10 0.56 0.64 0.08 0.75 0.83

P Value 0.818 0.750 0.457 0.426 0.773 0.390 0.365

1980-

2014

Zambia 4.562 3.658 6.114 3.283 0.988 4.071 1.961 2.935 1.038 3.799 2.011

F statistic 0.17 0.51 0.35 2.71 0.05 1.44 0.56 2.64 0.12 1.38

P Value 0.683 0.487 0.565 0.123 0.824 0.251 0.466 0.128 0.730 0.260 Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio. Average refers to the average value for these two ratios






∗ 𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation, interest payments abroad and the terms


𝜋𝐻𝐵𝑆𝐷𝐴𝑅𝑇, is the hypothetical income elasticity of demand from the balance of payments constrained growth model with sustainable debt accumulation, interest payments and the terms of trade





75

Appendix I

Regression results of the balance of payments constrained growth, 𝑦𝐵 , on the actual growth rate

Dependent

variable Constant, α

Coefficient on

the actual

growth rate, β R2 F statistic

Wald test 1

(β=1)

P value

Wald test 2

(α=0)

P value

𝒚𝑩 1.325 0.944** 0.178 4.34** 0.903 0.489

(1.881) (0.453)

𝒚𝑩 1.247*** 0.795 81.74*** 0.086*

(0.138)

∗ 𝒚𝑩 15.879** -2.219 0.146 2.40 0.041** 0.018**

(5.937) (1.432)

∗ 𝒚𝑩 1.392** 0.286 6.03** 0.499

(0.567)

Average 𝒚𝑩𝑺𝑫𝑨 9.529 0.205 0.000 0.00 0.824 0.523

(14.675) (3.535)

𝒚𝑩𝑺𝑫𝑨 2.391** 0.190 4.95** 0.209

(1.074)

𝒚𝑩𝑺𝑫𝑨𝑹 10.971 0.316 0.000 0.00 0.888 0.592

(20.166) (4.827)

𝒚𝑩𝑺𝑫𝑨𝑹 2.810* 0.152 3.60* 0.236

(1.482)

∗ 𝒚𝑩𝑺𝑫𝑨𝑹𝑻 7.195 -2.395 0.010 0.14 0.603 0.789

(26.454) (6.384)

∗ 𝒚𝑩𝑺𝑫𝑨𝑹𝑻 -0.758 0.008 0.14 0.407

(2.061)

𝒚𝑩𝑺𝑫𝑨𝑹𝑻 2.258 0.419 0.001 0.02 0.835 0.845

(11.417) (2.750)

𝒚𝑩𝑺𝑫𝑨𝑹𝑻 0.937 0.057 1.28 0.940

(0.828)

Start 𝒚𝑩𝑺𝑫𝑨 5.357 0.129 0.000 0.00 0.724 0.602

(10.116) (2.437)

𝒚𝑩𝑺𝑫𝑨 1.357* 0.138 3.38* 0.633

(0.738)

𝒚𝑩𝑺𝑫𝑨𝑹 5.398 0.107 0.000 0.00 0.728 0.616

(10.600) (2.537)

𝒚𝑩𝑺𝑫𝑨𝑹 1.334* 0.128 2.94* 0.671

(0.778)

∗ 𝒚𝑩𝑺𝑫𝑨𝑹𝑻 16.331 -2.430 0.174 2.95* 0.029** 0.014**

(5.860 (1.414)

∗ 𝒚𝑩𝑺𝑫𝑨𝑹𝑻 1.285** 0.254 5.12** 0.622

(0.567)

𝒚𝑩𝑺𝑫𝑨𝑹𝑻 4.912 0.237 0.001 0.02 0.648 0.480

(6.835) (1.646)

𝒚𝑩𝑺𝑫𝑨𝑹𝑻 1.363** 0.260 7.39** 0.476

(0.501) Note: Start refers to the start of period value for the share of exports in import ratio and the share of interest payments in imports ratio

Average refers to the average value for these two ratios for the period considered


76


∗ 𝑦𝐵,is the ‘strong’ original version of the balance of payments constrained growth model



∗ 𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments abroad and the terms


𝑦𝐵𝑆𝐷𝐴𝑅𝑇, is the balance of payments constrained growth with sustainable debt accumulation, interest payments and the terms of trade





Appendix J

The CUSUM and CUSUM squared graphs from the import demand and export demand functions

ordered by country.

Benin import demand function

Botswana export demand function

Botswana import demand function

CU

SU

M

Year

CUSUM

1980 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1980 2013

0

1

CU

SU

M

Year

CUSUM

1984 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1984 2013

0

1

CU

SU

M

Year

CUSUM

1991 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1991 2013

0

1

77

Cameroon export demand function

Cameroon import demand function

Chad export demand function

Chad import demand function

CU

SU

M

Year

CUSUM

1979 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1979 2013

0

1

CU

SU

M

Year

CUSUM

1974 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1974 2013

0

1

CU

SU

M

year

CUSUM

1977 2005

0 0

CU

SU

M s

qu

are

d

year

CUSUM squared

1977 2005

0

1

CU

SU

M

year

CUSUM

1978 2005

0 0

CU

SU

M s

qu

are

d

year

CUSUM squared

1978 2005

0

1

78

Democratic Republic of Congo export demand function

Democratic Republic of Congo import demand function

Republic of Congo export demand function

Republic of Congo import demand function

CU

SU

M

Year

CUSUM

1973 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1973 2013

0

1

CU

SU

M

Year

CUSUM

1978 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1978 2013

0

1

CU

SU

M

Year

CUSUM

1984 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1984 2013

0

1

CU

SU

M

Year

CUSUM

1999 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1999 2013

0

1

79

Gabon import demand function

Gambia export demand function

Gambia import demand function

Kenya export demand function

CU

SU

M

year

CUSUM

1969 2013

0 0

CU

SU

M s

qu

are

d

year

CUSUM squared

1969 2013

0

1

CU

SU

M

Year

CUSUM

1980 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1980 2013

0

1

CU

SU

M

Year

CUSUM

1979 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1979 2013

0

1

CU

SU

M

Year

CUSUM

1967 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1967 2013

0

1

80

Kenya import demand function

Mali export demand function

Mali import demand function

Mauritius export demand function

CU

SU

M

Year

CUSUM

1968 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1968 2013

0

1

CU

SU

M

Year

CUSUM

1988 2007

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1988 2007

0

1

CU

SU

M

Year

CUSUM

1978 2007

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1978 2007

0

1

CU

SU

M

Year

CUSUM

1989 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1989 2013

0

1

81

Mauritius import demand function

Mozambique export demand function

Mozambique import demand function

Export demand function Namibia

CU

SU

M

Year

CUSUM

1995 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1995 2013

0

1

CU

SU

M

Year

CUSUM

1988 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1988 2013

0

1

CU

SU

M

Year

CUSUM

1992 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1992 2013

0

1

CU

SU

M

Year

CUSUM

1995 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1995 2013

0

1

82

Namibia import demand function

Nigeria export demand function

Nigeria import demand function

Senegal export demand function

CU

SU

M

Year

CUSUM

1993 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1993 2013

0

1

CU

SU

M

Year

CUSUM

1999 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1999 2013

0

1

CU

SU

M

Year

CUSUM

1998 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1998 2013

0

1

CU

SU

M

Year

CUSUM

1979 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1979 2013

0

1

83

Senegal import demand function

Sierra Leone import demand function

South Africa export demand function

South Africa export demand function post-apartheid

CU

SU

M

Year

CUSUM

1974 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1974 2013

0

1

CU

SU

M

Year

CUSUM

1979 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1979 2013

0

1

CU

SU

M

Year

CUSUM

1973 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1973 2013

0

1

CU

SU

M

Year

CUSUM

1972 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1972 2013

0

1

84

South Africa import demand function

South Africa import demand function post-apartheid

South Africa import demand function with a trend

Sudan export demand function

CU

SU

M

Year

CUSUM

1969 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1969 2013

0

1

CU

SU

M

Year

CUSUM

1971 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1971 2013

0

1

CU

SU

M

Year

CUSUM

1973 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1973 2013

0

1

CU

SU

M

Year

CUSUM

1976 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1976 2013

0

1

85

Sudan import demand function

Uganda export demand function

Zambia export demand function

Zambia import demand function

CU

SU

M

Year

CUSUM

1966 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1970 2013

0

1

CU

SU

M

Year

CUSUM

1992 2014

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1992 2014

0

1

CU

SU

M

Year

CUSUM

1996 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1996 2013

0

1

CU

SU

M

Year

CUSUM

2002 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

2002 2013

0

1

86

Zimbabwe import demand function

Zimbabwe export demand function

CU

SU

M

Year

CUSUM

1989 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

1989 2013

0

1

CU

SU

M

Year

CUSUM

2002 2013

0 0

CU

SU

M s

qu

are

d

Year

CUSUM squared

2002 2013

0

1

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